Exhibit 99.1

RESMED ANNOUNCES RECORD FINANCIAL RESULTS FOR

QUARTER AND NINE MONTHS ENDED MARCH 31, 2004

SAN DIEGO, California, April 26, 2004…ResMed Inc. (NYSE: RMD) announced record revenue and income results for the quarter and nine months ended March 31, 2004. Revenue for the quarter was $91.3 million, an increase of 32% over the quarter ended March 31, 2003. Income from operations and net income for the March 31, 2004, quarter increased to $22.5 million and $15.0 million respectively, an increase of 31% and 23%. Earnings per share (on a diluted basis) for the quarter ended March 31, 2004, were $0.43, up from $0.35 per share in the March 2003 quarter. Gross margin was 63%, consistent with the March 2003 quarter.

Selling, general and administration (SG&A) costs for the quarter were $28.2 million, an increase of $7.2 million over the same period in fiscal 2003. The increase in SG&A related primarily to an increase in selling and administration personnel to meet expanding opportunities in the sleep-disordered breathing market. SG&A expenditure as a percentage of revenue was 31% in the March quarter compared to 30% in the same period in fiscal 2003.

Research and development expenditure, at approximately 8% of revenues, increased during the three months ended March 31, 2004, to $6.9 million from $5.1 million in the quarter ended March 31, 2003. The increase of 35% in R&D outlays reflects ResMed’s continuing commitment to clinical research and product development, particularly in the evolving cardiovascular area, as well as a stronger Australian dollar. In constant currency terms, research and development expenditure increased by 11% compared to March 2003 quarter. We expect to continue to spend approximately 8% of our revenues on R&D during the rest of the fiscal year.

For the nine months ended March 31, 2004, revenues were $246.4 million, an increase of 28% over the $192.9 million for the nine months ended March 31, 2003. Net income for the nine months ended March 31, 2004 was $41.4 million or $1.18 per share, compared with net income of $32.2 million or $0.94 per share for the same period in fiscal 2003. Net income increased by 29% over the prior year period.

Inventories at $57.5 million, increased marginally compared to December 2003 levels. Accounts receivable days sales outstanding, at 64 days, improved by 4 days, compared to the March 2003 quarter.

Peter C. Farrell PhD, Chairman and Chief Executive Officer, commented, “These record profit and revenue results for the March quarter of fiscal 2004 reflect ResMed’s continuing strong sales and profit growth in all major markets. Our operating cash flow for the March quarter was a record $27.2 million. Domestic sales increased by 33% over the March 2003 quarter to a record $45.1 million, reflecting continued healthy domestic demand for our sleep-disordered breathing products. International sales increased by 31% over the March 2003 quarter to $46.2 million, reflecting encouraging growth in major markets as well as a stronger Euro.”

Dr. Farrell further commented, “We continue to make progress in addressing those co-morbidites where there is a high prevalence of sleep-disordered breathing, particularly in the cardiovascular space. During the quarter, we again co-sponsored, with Guidant Corporation and MedCath Corporation, a satellite symposium on sleep-disordered breathing and cardiac disease during the annual American College of Cardiology’s annual meeting. Year over year attendance doubled, and the ACC ran a well-attended session on the same topic during its formal scientific meeting.”

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ResMed is a leading developer, manufacturer, and marketer of medical equipment for the diagnosis, treatment, and management of sleep-disordered breathing, selling a comprehensive range of products in over 60 countries.

ResMed will host a conference call at 1:30 p.m. Pacific Daylight Time (PDT) 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. Please allow extra time prior to the call to visit the 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) or +1 (617) 801-6888 (international) and entering conference ID No. 62611840.

Further information can be obtained by contacting David Pendarvis at ResMed Inc., San Diego, at (858) 746-2568; Adrian Smith at ResMed Limited Sydney on +61 (2) 9886-5407; 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 differ materially 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. & SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

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RESMED INC. & SUBSIDIARIES

Consolidated Balance Sheets (Unaudited)

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

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