Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND TWELVE MONTHS ENDED JUNE 30, 2012

SAN DIEGO, California, August 2, 2012 - ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended June 30, 2012. Revenue for the quarter ended June 30, 2012 was $371.9 million, a 9% increase (a 13% increase on a constant currency basis) over the quarter ended June 30, 2011. For the quarter ended June 30, 2012, net income was $76.8 million, an increase of 31% compared to the quarter ended June 30, 2011. Diluted earnings per share for the quarter ended June 30, 2012 were $0.53, an increase of 43% compared to the quarter ended June 30, 2011.

SG&A expenses were $105.9 million for the quarter ended June 30, 2012, an increase of $3.6 million, or 3% (a 9% increase on a constant currency basis) compared to the quarter ended June 30, 2011. SG&A costs were 28.5% of revenue in the quarter ended June 30, 2012, compared to 29.9% for the quarter ended June 30, 2011. SG&A expenses were favorably impacted by the depreciation of the Australian dollar and euro against the U.S. dollar.

R&D expenses were $27.9 million for the quarter ended June 30, 2012, or 7.5% of revenue. R&D expenses increased by 3% (a 10% increase on a constant currency basis) compared to the quarter ended June 30, 2011. R&D expenses were favorably impacted by the depreciation of the Australian dollar against the U.S. dollar.

The company amortized acquired intangibles of $2.9 million ($2.2 million, net of tax) during the quarter ended June 30, 2012. Stock-based compensation costs incurred during the quarter ended June 30, 2012 of $8.1 million ($5.9 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, 2012, revenue was $1.37 billion, an increase of 10% over the year ended June 30, 2011 (11% increase on a constant currency basis). For the year ended June 30, 2012, net income was $254.9 million, an increase of 12% compared to the year ended June 30, 2011. Diluted earnings per share for the year ended June 30, 2012 were $1.71, an increase of 19% compared to the year ended June 30, 2011.

Inventory, at $174.4 million, decreased by $26.4 million compared to June 30, 2011. Accounts receivable days sales outstanding, at 68 days, decreased by 1 day compared to June 30, 2011.

Additionally, our Board of Directors have today declared a quarterly dividend of $0.17 per share, which will have a record date of September 7, 2012, and be payable on September 28, 2012. The dividend will be paid in US currency to holders of our common stock trading on the New York Stock Exchange (NYSE). Holders of Chess Depositary Instruments (CDIs) trading on the Australian Stock Exchange, will receive an equivalent amount in Australian currency, based on the exchange rate on the record date, and reflecting the 10:1 ratio between CDIs and NYSE shares.

Peter C. Farrell Ph.D, chairman and chief executive officer, commented, “In the fourth quarter of fiscal 2012 we showed strong year-over-year growth on the top and bottom line and both our flow generator and mask categories did well. Revenue in Americas increased by 13% to $207.4 million over the prior year’s quarter. Revenue outside Americas increased by 3% to $164.5 million over the prior year’s quarter, or a 13% increase on a constant currency basis. Operating profit for the June quarter was $89.7 million and cash flow from operations was a robust $97.0 million, demonstrating excellent operating performance.

“‘The peer-reviewed literature continues to make it abundantly clear that untreated sleep-disordered breathing is, at best, seriously debilitating and, at worst, life-threatening. At the May Annual Meeting of the American Thoracic Society it was reported, by researchers from the University of Wisconsin, that individuals with untreated sleep apnea have a higher risk of dying from cancer and the risk was correlated with the severity of the disease. And, at the same meeting, it was also reported that untreated obstructive sleep apnea was independently correlated with diabetic peripheral neuropathy, a debilitating disease which causes severe pain in the hands and feet. Also, at this year’s Annual Endocrine Society meeting held in June, obstructive sleep apnea was found to be a frequent co-morbidity with polycystic ovary syndrome, a hormonal disorder which affects up to 10% of women of child-bearing

age. In addition, in the June 2012 issue of the European Heart Journal it was reported that any level of abnormal sleep-disordered breathing was associated with poor prognosis in chronic heart failure and that treatment of the sleep-disordered breathing with nocturnal ventilation significantly improved outcomes. Finally, in the July 2012 issue of the Journal of Cardiac Failure a study demonstrated the direct connection between untreated central sleep apnea and heart failure re-admission to hospital. These findings add to the continually mounting evidence connecting serious health disorders to untreated sleep-disordered breathing and point to the necessity of making the diagnosis and treatment of sleep-disordered breathing a standard of care in medical practice. In short, testing for sleep-disordered breathing should be as common as having one’s blood pressure taken.”

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. U.S. 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 617-597-5377 (domestic) or +1 617-597-5377 (international) and entering conference pass code no. 68952697. 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. 18538587.

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)

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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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