Exhibit 99.1

RESMED ANNOUNCES RECORD FINANCIAL RESULTS FOR

QUARTER AND NINE MONTHS ENDED MARCH 31, 2006

SAN DIEGO, California, May 4, 2006 - ResMed Inc. (NYSE: RMD) today announced record revenue and income results for the quarter ended March 31, 2006. Revenue for the quarter was $162.3 million, a 50% increase over the quarter ended March 31, 2005. For the current quarter, pro forma income from operations and pro forma net income were $42.0 million and $30.1 million, an increase of 47% and 59% respectively (pro forma measures exclude the impact of stock-based compensation costs, restructuring expenses, and amortization of acquired intangible assets, which are described below). Pro forma diluted earnings per share for the quarter ended March 31, 2006 were $0.39, an increase of 50%, compared to the March 2005 quarter. GAAP operating income was $36.7 million for the current quarter, while net income was $26.4 million or $0.34 per diluted share. Gross margin was 62% for the quarter ended March 31, 2006.

Pro forma selling, general and administration (SG&A) costs for the quarter were $50.1 million, an increase of $15.6 million, or 45%, over the same period in fiscal 2005. GAAP SG&A costs were $52.9 million for the quarter, an increase of $18.5 million, or 54%. The increase in SG&A was primarily due to recent acquisitions, the addition of selling and administration personnel, and infrastructure investment in Europe. Pro forma SG&A costs were 31% of revenue in the March quarter, compared to 32% in the same period in fiscal 2005. During the quarter, ResMed also donated $505,000 to the ResMed Foundations, which promote research and awareness of the serious medical consequences of untreated sleep-disordered breathing.

Research & development expenditure was $8.7 million for the quarter, excluding stock-based compensation costs. GAAP R&D expense during the quarter was $9.1 million or approximately 6% of revenue. GAAP R&D expenses increased 26% year over year and are expected to remain at about 6% of net revenue through the end of this fiscal year.

For the nine months ended March 31, 2006, revenue was $435.8 million, an increase of 45% over the $300.1 million for the nine months ended March 31, 2005. For the nine months ended March 31, 2006, pro forma income from operations and pro forma net income were $110.7 million and $77.6 million, an increase of 42% and 49% respectively. On a GAAP basis, income from operations was $93.5 million, while net income for the nine months ended March 31, 2006 was $65.1 million or $0.87 per diluted share.

Amortization of acquired intangibles of $1.6 million ($1.0 million net of tax), incurred during the quarter ended March 31, 2006 consisted of amortization of acquired intangible assets associated with our acquisitions of Resprecare, Hoefner, Saime, Pulmomed and PolarMed. Stock-based compensation costs incurred during the quarter ended March 31, 2006, of $3.7 million ($2.7 million net of tax), consisted of expenses associated with stock options granted to employees and the employee stock purchase plan. The recognition of these stock-based compensation expenses is in accordance with SFAS No. 123(R), which was adopted for the first time in the quarter ended September 30, 2005. No restructuring expenses were incurred during the quarter ended March 31, 2006.

The Company is providing tabular reconciliation of GAAP operating income and GAAP net income with pro forma operating income and pro forma net income, excluding the impact of stock-based compensation costs, restructuring expenses, and amortization of acquired intangibles, for the three month and nine month periods ended March 31, 2006 and March 31, 2005.

Inventory at $108.7 million, increased by $1.2 million compared to December 2005 levels. Accounts receivable days sales outstanding, at 68 days, decreased compared to the December 2005 quarter of 70 days.

Peter C. Farrell PhD, Chairman and Chief Executive Officer, commented, “In the third quarter of fiscal 2006, sales in the Americas increased by a record 49 percent over the year ago quarter to $86.2 million, reflecting continued strong demand for both our nasal and full face masks, and our S8™ flow generator platform. International sales, including incremental revenue contributions from the acquisitions of Resprecare, Hoefner, Saime, Pulmomed and PolarMed, totaled $76.1 million, a 51 percent increase over last year. Net income for the March quarter, excluding stock-based compensation costs, restructuring, and amortization of intangibles, was $30.1 million, an increase of 59 percent over the same period in 2005, driven primarily by strong sales growth. Our operating cash flow for the March quarter was a robust $32.8 million.”

Dr. Farrell continued, “We also remain encouraged with the progress we continue to make in targeting sleep-disordered breathing in heart failure, as well as in other co-morbidities. It is particularly encouraging for us to note that various affected medical specialties are gradually waking up to sleep and the impact that untreated sleep-disordered breathing is having on specific illnesses.”

About ResMed

ResMed is a leading manufacturer of medical equipment for the treatment and management of sleep-disordered breathing and other respiratory disorders. We are 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 for 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 2:00 p.m. U.S. Pacific Time today to discuss these quarterly results. Individuals wishing to access the conference call may do so via ResMed’s Web site at www.resmed.com or by dialing (866) 314-5232 (domestic) or +1 (617) 213-8052 (international) and entering participant passcode 90672494. 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 one hour 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 passcode 40216735.

Further information can be obtained by contacting Matthew Borer at ResMed Inc. San Diego (858) 746-2280; Brett Sandercock at ResMed Limited Sydney on (+61 2) 9886-5406; 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.

RESMED INC. & SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

RESMED INC. & SUBSIDIARIES

Consolidated Balance Sheets (Unaudited)

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

Reconciliation of Non-GAAP Financial Measures (Unaudited)

(Dollars in thousands except per share amounts)

In managing its business, ResMed makes use of certain non-GAAP financial measures in evaluating the Company’s results of operations. The measure, “pro forma operating income” is reconciled with GAAP operating income in the table below:

The measure, “pro forma net income” is reconciled with GAAP net income in the table below:

ResMed believes that presenting diluted earnings per share, excluding the impact of stock-based compensation costs, restructuring expenses and amortization of acquired intangible assets, is an additional measure of performance that investors can use to compare operating results between reporting periods. Management of the Company uses non-GAAP information internally in planning, forecasting, and evaluating the Company’s results of operations in the current period and in comparing it to past periods. The Company also uses these non-GAAP measures in evaluating management performance for compensation purposes. Management believes that this information also provides investors better insight in evaluating the Company’s earnings performance from core operations and provides consistency in financial reporting.

The Company initially adopted SFAS No. 123(R) on July 1, 2005 using the modified prospective method, which resulted in stock-based compensation expenses being recognized during the three months and nine months ended March 31, 2006 without corresponding expenses in the same periods in fiscal 2005. In addition, the events giving rise to the restructuring expenses are not associated with the Company’s normal operating business and are expected to result in future market opportunities, cost savings, and other benefits.

Management believes disclosure of non-GAAP earnings has economic substance because the excluded expenses represent non-cash expenditures, or relate to transactions that are variable in nature between reporting periods.

Our use of non-GAAP earnings is intended to supplement, and not to replace, our presentation of net income and other GAAP measures. Like all non-GAAP measures, non-GAAP earnings are subject to inherent limitations because they do not include all the expenses that must be included under GAAP. We compensate for the inherent limitations of non-GAAP measures by not relying exclusively on non-GAAP measures, but rather by using such information to supplement GAAP financial measures.

Reconciliation of Basic and Diluted Earnings per Share (Unaudited)

(Dollars in thousands except per share amounts)