Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER ENDED AND NINE MONTHS ENDED MARCH 31, 2011

SAN DIEGO, California, April 28, 2011 – ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended March 31, 2011. Revenue for the quarter ended March 31, 2011 was $313.3 million, a 12% increase (also a 12% increase on a constant currency basis) over the quarter ended March 31, 2010. For the quarter ended March 31, 2011, income from operations was $64.0 million and net income was $53.4 million, an increase of 5% and 9%, respectively, compared to the quarter ended March 31, 2010. Diluted earnings per share for the quarter ended March 31, 2011 were $0.34, an increase of 10% compared to the quarter ended March 31, 2010.

SG&A expenses were $92.5 million for the quarter ended March 31, 2011, an increase of $8.4 million, or 10% (an 8% increase on a constant currency basis) compared to the quarter ended March 31, 2010. SG&A costs were 29.5% of revenue in the quarter ended March 31, 2011, compared to 30.2% for the quarter ended March 31, 2010.

R&D expenses were $23.3 million for the quarter ended March 31, 2011, or 7.4% of revenue. R&D expenses increased by 28% (an 18% increase on a constant currency basis) compared to the quarter ended March 31, 2010. R&D expenses were negatively impacted by the appreciation of the Australian dollar against the U.S. dollar.

The company amortized acquired intangibles of $2.7 million ($1.8 million, net of tax) during the quarter ended March 31, 2011. Stock-based compensation costs incurred during the quarter ended March 31, 2011 of $6.8 million ($4.8 million, net of tax) consisted of expenses associated with stock options, restricted stock units, and our employee stock purchase plan.

For the nine months ended March 31, 2011, revenue was $901.3 million, an increase of 13% over the nine months ended March 31, 2010 (a 14% increase on a constant currency basis). For the nine months ended March 31, 2011, income from operations and net income were $200.2 million and $168.5 million, an increase of 17% and 23%, respectively, compared to the nine months ended March 31, 2010. Diluted earnings per share for the nine months ended March 31, 2011 were $1.07 per diluted share, an increase of 20% compared to the nine months ended March 31, 2010.

Inventory, at $205.0 million, increased by $19.4 million compared to June 30, 2010. Accounts receivable days sales outstanding, at 68 days, decreased by 3 days compared to June 30, 2010.

Peter C. Farrell PhD, Chairman and Chief Executive Officer, commented, “In the third quarter of fiscal 2011 we continued to show strong year-over-year growth especially in Europe and the Asia-Pacific region. Revenue outside the Americas increased by 16% to $152.7 million over the prior year’s quarter, or a 15% increase on a constant currency basis. Revenue in the Americas increased by over 9% to $160.5 million over the prior year’s quarter. Americas’ revenues continued to be adversely impacted by reduced bilevel sales, but we expect that the recent launch of the S9™ bilevel series will help to reverse this trend. Worldwide, our growth in flow generators was mainly driven by sales of the S9 AutoSet™. Patient interface sales did extremely well in all regions. With the recent launches of the Quattro™ FX full face mask and the Mirage™ FX nasal mask, we have completed the release of the trilogy of masks in the FX series. Operating profit for the March quarter was $64.0 million and cash flow from operations was a record $81.4 million, demonstrating excellent operating performance.

“We expect the growth of all our products to continue to benefit from the vastly under-penetrated and growing sleep-disordered breathing market. Due to the strong correlation between sleep-disordered breathing and comorbidities, such as heart disease and diabetes, chronic obstructive pulmonary disease, perioperative death and occupational health and safety, we believe that there are significant opportunities to further penetrate the market. In addition, findings from clinical studies continue to demonstrate the importance of diagnosing and treating sleep-disordered breathing. Increasingly, there is evidence coming to light that early intervention in the treatment of sleep-disordered breathing may slow or prevent the progression of chronic diseases.”

About ResMed

ResMed is a global leader in the development, manufacturing and marketing of medical products for the diagnosis, treatment and management of respiratory disorders, with a focus on sleep-disordered breathing. 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 617-614-4910 (domestic) or +1 617-614-4910 (international) and entering conference pass code no. 57596192. 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 617-801-6888 (domestic) and +1 617-801-6888 (international) and entering conference I.D. No. 68716093.

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 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 U.S. Securities & Exchange Commission. Those reports are available on the Company’s Website.

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RESMED INC AND SUBSIDIARIES

Condensed Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

All share and per share information has been adjusted to reflect the two-for-one stock split effected in the form of a 100% stock dividend that was declared on August 5, 2010 and distributed on August 30, 2010.

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RESMED INC AND SUBSIDIARIES

Condensed Consolidated Balance Sheets (Unaudited)

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

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