EXHIBIT 3.1

CERTIFICATE OF INCORPORATION, AS AMENDED

FIRST RESTATED CERTIFICATE OF INCORPORATION

OF

RESMED INC.

ResMed Inc., a corporation organized and existing under the laws of the State of Delaware (hereinafter referred to as the “Corporation”), hereby certifies as follows:

1. The name of the Corporation is ResMed Inc. The Corporation was originally incorporated under the name ResCare Medical Systems Ltd., and the original Certificate of Incorporation of the Corporation was filed with the Secretary of State of the State of Delaware on March 31, 1994.

2. Pursuant to Section 245 of the General Corporation Law of the State of Delaware, this First Restated Certificate of Incorporation only restates and integrates and does not further amend the provisions of the Certificate of Incorporation of the Corporation as theretofore amended or supplemented, and there is no discrepancy between those provisions and the provisions of this First Restated Certificate of Incorporation.

3. The text of the Certificate of Incorporation as heretofore amended or supplemented is hereby restated to read in its entirety as follows:

“FIRST: The name of the corporation is:

ResMed Inc. (hereinafter referred to as the “Corporation”).

SECOND: The address of the registered and principal office of the Corporation in this state is c/o 15 East North Street, in the City of Dover, County of Kent, State of Delaware 19901 and the name of the registered agent at said address is United Corporate Services, Inc.

THIRD: The purpose of the Corporation is to engage in any lawful act or activity for which corporations may be organized under the corporation laws of the State of Delaware.

FOURTH: a) The Corporation shall be authorized to issue the following shares of Capital Stock:

b) The designations and the powers, preferences and rights, and the qualifications or restrictions thereof are as follows:

The Preferred Stock shall be issued from time to time in one or more series, with such distinctive serial designations as shall be stated and expressed in the resolution or resolutions providing for the issue of such shares from time to time adopted by the Board of Directors; and in such resolution or resolutions providing for the issuance of shares of each particular series, the Board of Directors is expressly authorized to fix the annual rate or rates of the dividends for the particular series; the dividend payment dates for the particular series and the date from which dividends on all shares of such series issued prior to the record date for the first dividend payment date shall be cumulative; the redemption price or prices for the particular series; the voting powers for the particular series; the rights, if any, of the holders of the shares of the particular series to convert the same into shares of any other series or class or other securities of the Corporation, with any provisions for the subsequent adjustment of such conversion rights; and to classify or reclassify any unissued shares by fixing or altering from time to time any of the foregoing rights, privileges and qualifications.

All shares of Preferred Stock of any one series shall be identical with each other in all respects, except that shares of any one series issued at different times may differ as to the dates from which dividends thereon shall be cumulative; and all Preferred Stock shall be of equal rank, regardless of series, and shall be identical in all respects except as to the particulars fixed by the Board as hereinabove provided or as fixed herein.

The Certificate of Designations of Series A Junior Participating Preferred Stock attached hereto as Exhibit A is incorporated herein by reference (the “Amended Certificate of Designations”). The Amended Certificate of Designations restates the Certificate of Designations of Series A Junior Participating Preferred Stock, filed with the Secretary of State of the State of Delaware on March 18, 1999, to integrate only the Certificate of Increase in Authorized Number of Series A Junior Participating Preferred Stock, filed with the Secretary of State of the State of Delaware on October 1, 1999.

FIFTH: The following provisions are inserted for the management of the business and for the conduct of the affairs of the Corporation, and for further definition, limitation and regulation of the powers of the Corporation and of its directors and stockholders:

(1) The number of directors of the Corporation shall be such as from time to time shall be fixed by, or in the manner provided in the bylaws. Election of directors need not be by ballot unless the bylaws so provide.

(2) The Board of Directors shall have power without the assent or vote of the stockholders:

(a) To make, alter, amend, change, add to or repeal the Bylaws of the Corporation; to fix and vary the amount to be reserved for any proper purpose; to authorize and cause to be executed mortgages and liens upon all or any part of the property of the Corporation; to determine the use and disposition of any surplus or net profits; and to fix the times for the declaration and payment of dividends.

(b) To determine from time to time whether, and to what times and places, and under what conditions the accounts and books of the Corporation (other than the stock ledger) or any of them, shall be open to the inspection of the stockholders.

(3) The directors in their discretion may submit any contract or act for approval or ratification at any annual meeting of the stockholders or at any meeting of the stockholders called for the purpose of considering any such act or contract, and any contract or act that shall be approved or be ratified by the vote of the holders of a majority of the stock of the Corporation which is represented in person or by proxy at such meeting and entitled to vote thereat (provided that a lawful quorum of stockholders be there represented in person or by proxy) shall be as valid and as binding upon the Corporation and upon all the stockholders as though it had been approved or ratified by every stockholder of the Corporation, whether or not the contract or act would otherwise be open to legal attack because of directors’ interest, or for any other reason.

(4) In addition to the powers and authorities hereinbefore or by statute expressly conferred upon them, the directors are hereby empowered to exercise all such powers and do all such acts and things as may be exercised or done by the Corporation; subject, nevertheless, to the provisions of the statutes of Delaware, of this certificate, and to any bylaws from time to time made by the stockholders; provided, however, that no bylaws so made shall invalidate any prior act of the directors which would have been valid if such by-law had not been made.

SIXTH: No director shall be liable to the Corporation or any of its stockholders for monetary damages for breach of fiduciary duty as a director, except with respect to (1) a breach of the director’s duty of loyalty to the Corporation or its stockholders, (2) acts or omissions not in good faith or which involve intentional misconduct or a knowing violation of law, (3) liability under Section 174 of the Delaware General Corporation Law or (4) a transaction from which the director derived an improper personal benefit, it being

the intention of the foregoing provision to eliminate the liability of the Corporation’s directors to the Corporation or its stockholders to the fullest extent permitted by Section 102(b)(7) of the Delaware General Corporation Law, as amended from time to time. The Corporation shall indemnify to the fullest extent permitted by Sections 102(b)(7) and 145 of the Delaware General Corporation Law, as amended from time to time, each person that such Sections grant the Corporation power to indemnify.

SEVENTH: Whenever a compromise or arrangement is proposed between the Corporation and its creditors or any class of them and/or between the Corporation and its stockholders or any class of them, any court of equitable jurisdiction within the State of Delaware may, on the application in a summary way of the Corporation or of any creditor or stockholder thereof or on the application of any receiver or receivers appointed for the Corporation under the provisions of Section 291 of Title 8 of the Delaware Code or on the application of trustees in dissolution or of any receiver or receivers appointed for the Corporation under the provisions of Section 279 Title 8 of the Delaware Code, order a meeting of the creditors or class of creditors, and/or of the stockholders or class of stockholders of the Corporation, as the case may be, to be summoned in such manner as the said court directs. If a majority in number representing three-fourths (3/4) in value of the creditors or class of creditors, and/or of the stockholders or class of stockholders of the Corporation, as the case may be, agree to any compromise or arrangement and to any reorganization of the Corporation as consequence of such compromise or arrangement, the said compromise or arrangement and the said reorganization shall, if sanctioned by the court to which the said application has been made, be binding on all the creditors or class of creditors, and/or on all the stockholders or class of stockholders, of the Corporation, as the case may be, and also on the Corporation.

EIGHTH: The Corporation reserves the right to amend, alter, change or repeal any provision contained in this certificate of incorporation in the manner now or hereafter prescribed by law, and all rights and powers conferred herein on stockholders, directors and officers are subject to this reserved power.”

IN WITNESS WHEREOF, the Corporation has caused this First Restated Certificate of Incorporation to be signed by Peter C. Farrell, its Chief Executive Officer and President, this 5^th day of March, 2001.

EXHIBIT A

AMENDED CERTIFICATE OF DESIGNATIONS

OF

SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

OF

RESMED INC.

(Pursuant to Section 151 of the Delaware General Corporation Law)

RESMED INC., a corporation organized and existing under the General Corporation Law of the State of Delaware (hereinafter called the “Corporation”), hereby certifies that the following resolution was adopted by the Board of Directors of the Corporation as required by Section 151 of the General Corporation Law at a meeting duly called and held on April 15, 1997, and was amended, as set forth herein, to increase the authorized number of Series A Junior Participating Preferred Stock from 150,000 to 250,000 shares on October 1, 1999.

RESOLVED, that pursuant to the authority granted to and vested in the Board of Directors of this Corporation (hereinafter called the “Board of Directors” or the “Board”) in accordance with the provisions of the Certificate of Incorporation, the Board of Directors hereby creates a series of Preferred Stock, par value $.01 per share (the “Preferred Stock”), of the Corporation and hereby states the designation and number of shares, and fixes the relative rights, preferences, and limitations thereof as follows:

Series A Junior Participating Preferred Stock:

Section 1. Designation and Amount. The shares of such series shall be designated as “Series A Junior Participating Preferred Stock” (the “Series A Preferred Stock”) and the number of shares constituting the Series A Preferred Stock shall be 250,000. Such number of shares may be increased or decreased by resolution of the Board of Directors; provided, that no decrease shall reduce the number of shares of Series A Preferred Stock to a number less than the number of shares then outstanding plus the number of shares reserved for issuance upon the exercise of outstanding options, rights or warrants or upon the conversion of any outstanding securities issued by the Corporation convertible into Series A Preferred Stock.

Section 2. Dividends and Distributions.

(A) Subject to the rights of the holders of any shares of any series of Preferred Stock (or any similar stock) ranking prior and superior to the Series A Preferred Stock with respect to dividends, the holders of shares of Series A Preferred Stock, in preference to the holders of Common Stock, par value $.004 per share (the “Common Stock”), of the Corporation, and of any other junior stock, shall be entitled to receive, when, as and if declared by the Board of Directors out of funds legally available for the purpose, quarterly dividends payable in cash on the first day of March, June, September and December in each year (each such date being referred to herein as a “Quarterly Dividend Payment Date”), commencing on the first Quarterly Dividend Payment Date after the first issuance of a share or fraction of a share of Series A Preferred Stock, in an amount per share (rounded to the nearest cent) equal to the greater of (a) $1.00 or (b) subject to the provision for adjustment hereinafter set forth, 100 times the aggregate per share amount of all cash dividends, and 100 times the aggregate per share amount (payable in kind) of all non-cash dividends or other distributions, other than a dividend payable in shares of Common Stock or a subdivision of the outstanding shares of Common Stock (by reclassification or otherwise), declared on the Common Stock since the immediately preceding Quarterly Dividend Payment Date or, with respect to the first Quarterly Dividend Payment Date, since the first issuance of any share or fraction of a share of Series A Preferred Stock. In the event the Corporation shall at any time declare or pay any dividend on the Common Stock payable in shares of Common Stock, or effect a subdivision, combination or consolidation of the outstanding shares of Common Stock (by reclassification or otherwise than by payment of a dividend in shares of Common Stock) into a greater or lesser number of shares of Common Stock, then in each such case the amount to which holders of shares of Series A Preferred Stock were entitled immediately prior to such event

under clause (b) of the preceding sentence shall be adjusted by multiplying such amount by a fraction, the numerator of which is the number of shares of Common Stock outstanding immediately after such event and the denominator of which is the number of shares of Common Stock that were outstanding immediately prior to such event.

(B) The Corporation shall declare a dividend or distribution on the Series A Preferred Stock as provided in paragraph (A) of this Section 2 immediately after it declares a dividend or distribution on the Common Stock (other than a dividend payable in shares of Common Stock); provided that, in the event no dividend or distribution shall have been declared on the Common Stock during the period between any Quarterly Dividend Payment Date and the next subsequent Quarterly Dividend Payment Date, a dividend of $1.00 per share on the Series A Preferred Stock shall nevertheless be payable on such subsequent Quarterly Dividend Payment Date.

(C) Dividends shall begin to accrue and be cumulative on outstanding shares of Series A Preferred Stock from the Quarterly Dividend Payment Date next preceding the date of issue of such shares, unless the date of issue of such shares is prior to the record date for the first Quarterly Dividend Payment Date, in which case dividends on such shares shall begin to accrue from the date of issue of such shares, or unless the date of issue is a Quarterly Dividend Payment Date or is a date after the record date for the determination of holders of shares of Series A Preferred Stock entitled to receive a quarterly dividend and before such Quarterly Dividend Payment Date, in either of which events such dividends shall begin to accrue and be cumulative from such Quarterly Dividend Payment Date. Accrued but unpaid dividends shall not bear interest. Dividends paid on the shares of Series A Preferred Stock in an amount less than the total amount of such dividends at the time accrued and payable on such shares shall be allocated pro rata on a share-by-share basis among all such shares at the time outstanding. The Board of Directors may fix a record date for the determination of holders of shares of Series A Preferred Stock entitled to receive payment of a dividend or distribution declared thereon, which record date shall be not more than 60 days prior to the date fixed for the payment thereof.

Section 3. Voting Rights. The holders of shares of Series A Preferred Stock shall have the following voting rights:

(A) Subject to the provision for adjustment hereinafter set forth, each share of Series A Preferred Stock shall entitle the holder thereof to 100 votes on all matters submitted to a vote of the stockholders of the Corporation. In the event the Corporation shall at any time declare or pay any dividend on the Common Stock payable in shares of Common Stock, or effect a subdivision, combination or consolidation of the outstanding shares of Common Stock (by reclassification or otherwise than by payment of a dividend in shares of Common Stock) into a greater or lesser number of shares of Common Stock, then in each such case the number of votes per share to which holders of shares of Series A Preferred Stock were entitled immediately prior to such event shall be adjusted by multiplying such number by a fraction, the numerator of which is the number of shares of Common Stock outstanding immediately after such event and the denominator of which is the number of shares of Common Stock that were outstanding immediately prior to such event.

(B) Except as otherwise provided herein, in any other Certificate of Designations creating a series of Preferred Stock or any similar stock, or by law, the holders of shares of Series A Preferred Stock and the holders of shares of Common Stock and any other capital stock of the Corporation having general voting rights shall vote together as one class on all matters submitted to a vote of stockholders of the Corporation.

(C) Except as set forth herein, or as otherwise provided by law, holders of Series A Preferred Stock shall have no special voting rights and their consent shall not be required (except to the extent they are entitled to vote with holders of Common Stock as set forth herein) for taking any corporate action.

Section 4. Certain Restrictions.

(A) Whenever quarterly dividends or other dividends or distributions payable on the Series A Preferred Stock as provided in Section 2 are in arrears, thereafter and until all accrued and unpaid dividends and distributions, whether or not declared, on shares of Series A Preferred Stock outstanding shall have been paid in full, the Corporation shall not:

(i) declare or pay dividends, or make any other distributions, on any shares of stock ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series A Preferred Stock;

(ii) declare or pay dividends, or make any other distributions, on any shares of stock ranking on a parity (either as to dividends or upon liquidation, dissolution or winding up) with the Series A Preferred Stock, except dividends paid ratably on the Series A Preferred Stock and all such parity stock on which dividends are payable or in arrears in proportion to the total amounts to which the holders of all such shares are then entitled;

(iii) redeem or purchase or otherwise acquire for consideration shares of any stock ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series A Preferred Stock, provided that the Corporation may at any time redeem, purchase or otherwise acquire shares of any such junior stock in exchange for shares of any stock of the Corporation ranking junior (either as to dividends or upon dissolution, liquidation or winding up) to the Series A Preferred Stock; or

(iv) redeem or purchase or otherwise acquire for consideration any shares of Series A Preferred Stock, or any shares of stock ranking on a parity with the Series A Preferred Stock, except in accordance with a purchase offer made in writing or by publication (as determined by the Board of Directors) to all holders of such shares upon such terms as the Board of Directors, after consideration of the respective annual dividend rates and other relative rights and preferences of the respective series and classes, shall determine in good faith will result in fair and equitable treatment among the respective series or classes.

(B) The Corporation shall not permit any Subsidiary of the Corporation to purchase or otherwise acquire for consideration any shares of stock of the Corporation unless the Corporation could, under paragraph (A) of this Section 4, purchase or otherwise acquire such shares at such time and in such manner.

Section 5. Reacquired Shares. Any shares of Series A Preferred Stock purchased or otherwise acquired by the Corporation in any manner whatsoever shall be retired and canceled promptly after the acquisition thereof. All such shares shall upon their cancellation become authorized but unissued shares of Preferred Stock and may be reissued as part of a new series of Preferred Stock subject to the conditions and restrictions on issuance set forth herein, in the Certificate of Incorporation, or in any other Certificate of Designations creating a series of Preferred Stock or any similar stock or as otherwise required by law.

Section 6. Liquidation, Dissolution or Winding Up. Upon any liquidation, dissolution or winding up of the Corporation, no distribution shall be made (1) to the holders of shares of stock ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series A Preferred Stock unless, prior thereto, the holders of shares of Series A Preferred Stock shall have received $100 per share, plus an amount equal to accrued and unpaid dividends and distributions thereon, whether or not declared, to the date of such payment, provided that the holders of shares of Series A Preferred Stock shall be entitled to receive an aggregate amount per share, subject to the provision for adjustment hereinafter set forth, equal to 100 times the aggregate amount to be distributed per share to holders of shares of Common Stock, or (2) to the holders of shares of stock ranking on a parity (either as to dividends or upon liquidation, dissolution or winding up) with the Series A Preferred Stock, except distributions made ratably on the Series A Preferred Stock and all such parity stock in proportion to the total amounts to which the holders of all such shares are entitled upon such liquidation, dissolution or winding up. In the event the Corporation shall at any time declare or pay any dividend on the Common Stock payable in shares of Common Stock, or effect a subdivision, combination or consolidation of the outstanding shares of Common Stock (by reclassification or otherwise than by payment of a dividend in shares of Common Stock) into

a greater or lesser number of shares of Common Stock, then in each such case the aggregate amount to which holders of shares of Series A Preferred Stock were entitled immediately prior to such event under the proviso in clause (1) of the preceding sentence shall be adjusted by multiplying such amount by a fraction the numerator of which is the number of shares of Common Stock outstanding immediately after such event and the denominator of which is the number of shares of Common Stock that are outstanding immediately prior to such event.

Section 7. Consolidation, Merger, etc. In case the Corporation shall enter into any consolidation, merger, combination or other transaction in which the shares of Common Stock are exchanged for or changed into other stock or securities, cash and/or any other property, then in any such case each share of Series A Preferred Stock shall at the same time be similarly exchanged or changed into an amount per share, subject to the provision for adjustment hereinafter set forth, equal to 100 times the aggregate amount of stock, securities, cash and/or any other property (payable in kind), as the case may be, into which or for which each share of Common Stock is changed or exchanged. In the event the Corporation shall at any time declare or pay any dividend on the Common Stock payable in shares of Common Stock, or effect a subdivision, combination or consolidation of the outstanding shares of Common Stock (by reclassification or otherwise than by payment of a dividend in shares of Common Stock) into a greater or lesser number of shares of Common Stock, then in each such case the amount set forth in the preceding sentence with respect to the exchange or change of shares of Series A Preferred Stock shall be adjusted by multiplying such amount by a fraction, the numerator of which is the number of shares of Common Stock outstanding immediately after such event and the denominator of which is the number of shares of Common Stock that were outstanding immediately prior to such event.

Section 8. No Redemption. The shares of Series A Preferred Stock shall not be redeemable.

Section 9. Rank. The Series A Preferred Stock shall rank, with respect to the payment of dividends and the distribution of assets, junior to all series of any other class of the Corporation’s Preferred Stock, except to the extent that any such other series specifically provides that it shall rank on a parity with or junior to the Series A Preferred Stock.

Section 10. Amendment. The Certificate of Incorporation of the Corporation shall not be amended in any manner which would materially alter or change the powers, preferences or special rights of the Series A Preferred Stock so as to affect them adversely without the affirmative vote of the holders of at least two-thirds of the outstanding shares of Series A Preferred Stock, voting together as a single class.

IN WITNESS WHEREOF, the Corporation has caused this Amended Certificate of Designations of Series A Junior Participating Preferred Stock to be signed by Peter C. Farrell, its Chief Executive Officer and President, this 5th day of March, 2001.

CERTIFICATE OF AMENDMENT

OF THE RESTATED

CERTIFICATE OF INCORPORATION

OF

RESMED INC.,

A DELAWARE CORPORATION

ResMed Inc., a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (this “Corporation”), DOES HEREBY CERTIFY:

1. The name of the Corporation is ResMed Inc. The Corporation was originally incorporated under the name ResCare Medical Systems Ltd., and the original Certificate of Incorporation of the Corporation was filed with the Secretary of State of the State of Delaware on March 31, 1994.

2. That the Board of Directors of this Corporation, acting pursuant to the authority of Section 141(f) of the General Corporation Law of the State of Delaware, adopted a resolution setting forth a proposed amendment of the Certificate of Incorporation of this Corporation. The resolution setting forth the proposed amendment is as follows:

“NOW, THEREFORE, BE IT RESOLVED, that the Restated Certificate of Incorporation of this Corporation be amended by changing the first paragraph of Article Fourth thereof so that, as amended, the first paragraph of Article Fourth shall read in its entirety as follows:

“FOURTH: a) The Corporation shall be authorized to issue the following shares of Capital Stock:

3. This Amendment of the Restated Certificate of Incorporation was duly adopted by the holders of a majority of the issued and outstanding shares of the Common Stock of the Corporation, par value $0.004 per share, in accordance with the provisions of Sections 222 and 242 of the General Corporation Law of the State of Delaware.

IN WITNESS WHEREOF the undersigned has caused this Certificate of Amendment to be duly executed as of the 9th day of May, 2006.