Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND TWELVE MONTHS ENDED JUNE 30, 2010

*RESMED ALSO ANNOUNCES TWO-FOR-ONE STOCK SPLIT

SAN DIEGO, California, August 5, 2010 – ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended June 30, 2010, and a two-for-one stock split.

Financial Results

Revenue for the quarter ended June 30, 2010 was $291.6 million, a 16% increase (an 18% increase on a constant currency basis) over the quarter ended June 30, 2009. For the quarter ended June 30, 2010, income from operations was $68.6 million and net income was $53.2 million, an increase of 19% and 17%, respectively, compared to the quarter ended June 30, 2009. Diluted earnings per share for the quarter ended June 30, 2010 were $0.68, an increase of 15% compared to the quarter ended June 30, 2009.

SG&A expenses were $83.9 million for the quarter ended June 30, 2010, an increase of $6.3 million, or 8% (a 9% increase on a constant currency basis) over the quarter ended June 30, 2009. The increase in SG&A was primarily due to expenses necessary to support sales growth. SG&A costs were 29% of revenue in the quarter ended June 30, 2010, compared to 31% in the quarter ended June 30, 2009.

R&D expenses were $20.0 million for the quarter ended June 30, 2010, or 7% of revenue. R&D expenses increased by 18% (a 9% increase on a constant currency basis) compared to the quarter ended June 30, 2009. R&D expenses were negatively impacted by the depreciation of the U.S. dollar against the Australian dollar.

The company amortized acquired intangibles of $2.1 million ($1.4 million, net of tax) during the quarter ended June 30, 2010. Stock-based compensation costs incurred during the quarter ended June 30, 2010 of $7.9 million ($5.3 million, net of tax) consisted of expenses associated with stock options, restricted stock units, and our employee stock purchase plan.

For the year ended June 30, 2010, revenue was $1.1 billion, a 19% increase (a 17% increase on a constant currency basis) over the year ended June 30, 2009. For the year ended June 30, 2010, income from operations was $240.4 million and net income was $190.1 million, an increase of 26% and 30%, respectively, compared to the year ended June 30, 2009. Diluted earnings per share for the year ended June 30, 2010 were $2.45, an increase of 29% compared to the year ended June 30, 2009.

Inventory, at $185.6 million, increased by $28.2 million compared to June 30, 2009. Accounts receivable days sales outstanding, at 71 days, decreased by 3 days compared to June 30, 2009.

Kieran T. Gallahue, President and Chief Executive Officer, commented, “In the fourth quarter of fiscal 2010, we continued to show strong growth year-over-year in the Americas, as well as in international markets. Our favorable mix of product sales and market share gains led to a 20% revenue increase in the Americas over the prior year’s quarter, resulting in $160.9 million in sales. Revenue outside the Americas increased by 11% to $130.7 million over the prior year’s quarter, or a 16% increase on a constant currency basis. Globally, our growth in flow generators was mainly driven by strong sales of the new S9™ AutoSet and Elite products. Mask sales were particularly robust this quarter across all categories and across all geographies. Operating profit for the June quarter was $68.6 million and cash flow from operations was $59.0 million, demonstrating excellent operating performance.

“Surpassing the billion dollar mark in annual sales is a result of our ability to continue to innovate and launch new products to treat sleep-disordered breathing. We believe continued growth will also come from the increasing confirmation of the strong impact of the relationship between sleep-disordered breathing, obstructive sleep apnea and co-morbidities such as cardiac disease, diabetes, hypertension and obesity. In a recently released study in Circulation, it was shown that obstructive sleep apnea is associated with an increased risk of incident heart failure in a general community of middle-aged and older men. Specifically, men ages 40-70 with AHI ³30 were 68% more likely to develop coronary heart disease than those with AHI<5. This adds to a

multitude of studies being conducted that provide abundant new evidence that treating sleep-disordered breathing and obstructive sleep apnea can improve health, quality of life and also mitigate the dangers of sleep apnea in occupational health and safety, especially in the transport industry.”

Stock Split

ResMed Inc. also announced today that its board of directors approved a two-for-one stock split of the company’s outstanding shares of common stock, payable in the form of a 100% stock dividend.

Stockholders of record on the New York Stock Exchange at the close of trading on August 17, 2010 will receive one additional share of common stock for each share held on that date. The common stock will be distributed to shareholders on or about August 30, 2010, by ResMed’s NYSE transfer agent, American Stock Transfer and Trust Company, LLC. The common stock is expected to begin trading on a post-split basis on the NYSE beginning on August 31, 2010 or one day following the distribution date.

Holders of CHESS Depositary Interests (CDIs) on the Australian Stock Exchange (ASX) will also receive a bonus issue of one additional CDI for every CDI held on the ASX record date of August 18, 2010. Unlike the shares on the NYSE, the existing CDIs are expected to be quoted on an “ex-bonus” basis on August 12, 2010 on the ASX (ASX Code: RMD), and bonus CDI’s will be quoted on a deferred settlement basis (ASX Code: RMDBN). ResMed is seeking a waiver from the ASX that would, if granted, suspend the conversion of shares between the NYSE common stock and ASX CDIs during the time period between August 12^th and August 31^st. The bonus CDIs will be distributed by ResMed’s ASX share registry, Computershare Limited, on or about August 31, 2010, and normal trading will begin on the following day.

“Our strong financial performance can be attributed to the growth and strength of our business and consistent execution and as a result, we felt it was in the best interest of our shareholders to declare a stock split,” commented Mr. Gallahue. “ResMed has delivered an outstanding return for our shareholders and the split is designed to improve liquidity and broaden ownership in our company.”

As of July 30, 2010, ResMed had common stock outstanding of approximately 76 million shares. Following the stock distribution, the number of outstanding shares will increase to approximately 152 million shares.

About ResMed

ResMed is a leading developer, manufacturer and distributor of medical equipment for treating, diagnosing, and managing sleep-disordered breathing and other respiratory disorders. The company is dedicated to developing innovative products to improve the lives of those who suffer from these conditions and to increasing awareness among patients and healthcare professionals of the potentially serious health consequences of untreated sleep-disordered breathing. For more information on ResMed, visit www.resmed.com.

ResMed will host a conference call at 1:30 p.m. US Pacific Time today to discuss these quarterly results. Individuals wishing to access the conference call may do so via ResMed’s Website at www.resmed.com or by dialing (800) 299-8538 (domestic) or +1 (617) 786-2902 (international) and entering conference I.D. No. 86087175. Please allow extra time prior to the call to visit the Web site and download the streaming media player (Windows Media Player) required to listen to the Internet broadcast. The online archive of the broadcast will be available approximately 90 minutes after the live call and will be available for two weeks. A telephone replay of the conference call is available by dialing (888) 286-8010 (domestic) and +1 (617) 801-6888 (international) and entering conference I.D. No. 89978676.

Further information can be obtained by contacting Constance Bienfait at ResMed Inc., San Diego, at (858) 836-5971; Brett Sandercock at ResMed Limited, Sydney, on (+612) 8884-2090; or by visiting the Company’s multilingual Web site at www.resmed.com.

Statements contained in this release that are not historical facts are “forward-looking” statements as contemplated by the Private Securities Litigation Reform Act of 1995. These forward-looking statements, including statements regarding the Company’s future revenue, earnings or expenses, new product development and new markets for the Company’s products, are subject to risks and uncertainties, which could cause actual results to materially differ from those projected or implied in the forward-looking statements. Those risks and uncertainties are discussed in the Company’s Annual Report on Form 10-K for its most recent fiscal year and in other reports the Company files with the U.S. Securities & Exchange Commission. Those reports are available on the Company’s Web site.

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RESMED INC AND SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

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RESMED INC AND SUBSIDIARIES

Consolidated Balance Sheets (Unaudited)

(In US$ thousands except share and per share data)

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