Exhibit 99.1

RESMED INC ANNOUNCES RECORD FINANCIAL RESULTS

FOR QUARTER AND YEAR ENDED JUNE 30, 2005

SAN DIEGO, California, August 22, 2005- ResMed Inc (NYSE: RMD) today announced record revenue and income results for the quarter and year ended June 30, 2005. Revenues for the June 30, 2005 quarter were $125.4 million, a 35% increase over the quarter ended June 30, 2004. Excluding the incremental revenue contribution from acquisitions, revenue was $116.4 million, an increase of 25%. For the June 30, 2005 quarter, income from operations and net income, both excluding the impact of restructuring expenses and acquisition related costs described below, were $30.4 million and $21.7 million, an increase of 24% and 37% respectively. Diluted earnings per share, excluding the impact of restructuring expenses and acquisition related costs, for the quarter ended June 30, 2005 were $0.60, an increase of 33%, compared to the June 30, 2004 quarter. Net income for the June quarter was $15.6 million or $0.43 per diluted share including after-tax restructuring expenses and acquisition related costs of $6.2 million. Gross margin was 64% for the quarter ended June 30, 2005, consistent with the quarter ended June 30, 2004.

Selling, general and administration (SG&A) costs for the quarter were $41.2 million, an increase of $12.7 million over the same period in fiscal 2004. SG&A increased as a result of the acquisition of Saime in May, the addition of selling and administration personnel, and infrastructure investment in Europe. SG&A expenditure as a percentage of revenue was 33% in the June quarter, compared to 31% in the same period in fiscal 2004.

Research and development expenditure at approximately 6% of revenues, increased during the three months ended June 30, 2005, to $8.1 million from $6.5 million in the quarter ended June 30, 2004. The increase reflects ResMed’s continuing commitment to clinical research and product development. ResMed intends to continue to spend approximately 6% to 7% of revenues on R&D during fiscal year 2006.

Company revenues for fiscal year 2005 were $425.5 million, an increase of 25% over the year ended June 30, 2004. Excluding the incremental revenue contribution from acquisitions, revenue was $414.0 million, an increase of 22%. Excluding the impact of restructuring expenses and acquisition related costs, net income for the year was $74.2 million or $2.07 per share, an increase of 29% compared with net income of $57.6 million or $1.64 per share for fiscal year 2004.

Restructuring expenses incurred during the quarter ended June 30, 2005 of $0.6 million ($0.4 million net of tax) consisted of expenses associated with the previously-announced integration of the Company’s German operations. Acquisition related expenses of $6.7 million ($6.2 million net of tax) incurred during the quarter ended June 30, 2005 consisted of expenses associated with our acquisitions of Resprecare, Hoefner and Saime comprising $0.8 million amortization of acquired intangible assets and a one-time in-process research and development charge of $5.3 million associated with our acquisition of Saime.

With the financial information included in this press release, the Company is providing a tabular reconciliation of GAAP operating income and GAAP net income with operating income, and net income, excluding the impact of restructuring expenses, donations to the foundations, amortization of acquired intangibles and an in-process research and development charge for the quarters and years ended June 30, 2005 and June 30, 2004.

Inventory at $89.1 million, increased by $13.6 million compared to March 2005 levels, reflecting the inclusion of Saime inventory and increases to support volume growth in sales. Accounts receivable days sales outstanding, at 71 days, were consistent with the March 2005 quarter.

Peter C. Farrell Ph.D., Chairman and Chief Executive Officer, commented, “Fiscal 2005 was another successful year for ResMed, and our financial results certainly reflect that. The launch of the Mirage Swift patient interface, the acquisition of Saime, and the roll-out of the new S8 platform, have delivered strong revenue and profit results this year and, more importantly, have positioned us well for further growth. In the fourth quarter, domestic sales increased by a very robust 37% over the year ago quarter to $62.2 million, reflecting strong demand for our new Mirage Swift patient interface and full face mask as well as a favorable reception to the S8 Escape flow generator, which was initially released into the domestic market. Organically, international sales increased to $54.1 million, an encouraging 14% growth compared to the June 2004 quarter. Including incremental revenue contributions from the acquisitions of Resprecare, Hoefner and Saime, international sales totaled $63.2 million, a 33% increase over last year. Net income for the June quarter, excluding restructuring and acquisition-related expenses, was $21.7 million, an increase of 37% over the same period in 2004, due to strong sales growth and a lower effective tax rate in the June quarter. Our operating cash flow for the June quarter was an encouraging $21.3 million.”

Dr. Farrell further continued, “In June, ResMed was included on BusinessWeek’s list of the Best Small Companies for the sixth time in the last seven years, based on our three-year results in sales growth, earnings growth, and return on invested capital. This year we made great progress in putting the fundamentals in place to continue our history of financial growth. Our team has continued to deliver outstanding new products to the market, identified acquisition opportunities to expand our international operations, and strenghtened our efforts to increase education and awareness of sleep-disordered breathing. We aim to continue these efforts.”

ResMed will host a conference call at 2:00 p.m. U.S. Pacific Daylight Time (USPDT) 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 (866) 203-2528 (domestic) or +1 (617) 213-8847 (international) and entering conference I.D. No. 1788883. Please allow extra time prior to the call to visit the Website 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. 99737510.

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 of the potentially serious health consequences of untreated sleep-disordered breathing. For more information on ResMed, visit www.resmed.com.

Further information can be obtained by contacting Hillary Theakston at ResMed Inc San Diego at (858) 746-2610; Adrian Smith at ResMed Limited Sydney on (+61 2) 9886-5406; or by visiting the Company’s multilingual Website 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 US Securities & Exchange Commission. Those reports are available on the Company’s Website.

RESMED INC AND SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

RESMED INC AND 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, “operating income, excluding the impact of restructuring expenses, donation to foundations, amortization of acquired intangible assets and IPR&D charge” is reconciled with GAAP operating income in the table below:

The measure, “net income, excluding the impact of restructuring expenses, donation to foundations, amortization of acquired intangible assets and IPR&D charge” is reconciled with GAAP net income in the table below:

ResMed believes that presenting diluted earnings per share, excluding the impact of restructuring expenses and donation to foundation, is an additional measure of performance that investors can use to compare operating results between reporting periods. Management of the Company uses this information in evaluating the Company’s results of operations and believes that this information also provides investors better insight in evaluating the Company’s earnings performance from core operations. The events giving rise to these restructuring expenses and donation to foundation are not associated with the Company’s normal operating business and are expected to result in future market opportunities, cost savings, and other benefits.

Reconciliation of Basic and Diluted Earnings per Share (Unaudited)

(Dollars in thousands, except per share amounts)