Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND TWELVE MONTHS ENDED JUNE 30, 2011

- ResMed also Announces Acquisition of Gründler GmbH

SAN DIEGO, California, August 4, 2011 - ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended June 30, 2011. Revenue for the quarter ended June 30, 2011 was $341.9 million, a 17% increase (an 11% increase on a constant currency basis) over the quarter ended June 30, 2010. For the quarter ended June 30, 2011, net income was $58.5 million, an increase of 10% compared to the quarter ended June 30, 2010. Diluted earnings per share for the quarter ended June 30, 2011 were $0.37, an increase of 9% compared to the quarter ended June 30, 2010.

SG&A expenses were $102.3 million for the quarter ended June 30, 2011, an increase of $18.5 million, or 22% (a 13% increase on a constant currency basis) compared to the quarter ended June 30, 2010. SG&A costs were 29.9% of revenue in the quarter ended June 30, 2011, compared to 28.8% for the quarter ended June 30, 2010. SG&A expenses were negatively impacted by the appreciation of the Australian dollar and euro against the U.S. dollar.

R&D expenses were $27.0 million for the quarter ended June 30, 2011, or 7.9% of revenue. R&D expenses increased by 35% (an 11% increase on a constant currency basis) compared to the quarter ended June 30, 2010. R&D expenses were primarily impacted by the appreciation of the Australian dollar and euro against the U.S. dollar.

The company amortized acquired intangibles of $2.9 million ($1.9 million, net of tax) during the quarter ended June 30, 2011. Stock-based compensation costs incurred during the quarter ended June 30, 2011 of $7.5 million ($5.4 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, 2011, revenue was $1.2 billion, an increase of 14% over the year ended June 30, 2010 (a 13% increase on a constant currency basis). For the year ended June 30, 2011, net income was $227.0 million, an increase of 19% compared to the year ended June 30, 2010. Diluted earnings per share for the year ended June 30, 2011 were $1.44, an increase of 17% compared to the year ended June 30, 2010.

Inventory, at $200.8 million, increased by $15.1 million compared to June 30, 2010. Accounts receivable days sales outstanding, at 69 days, decreased by 2 days compared to June 30, 2010.

Peter C. Farrell Ph.D, chairman and chief executive officer, commented, “In the fourth quarter of fiscal 2011 we continued to show strong year-over-year growth. Revenue in Americas increased by 14% to $182.8 million over the prior year’s quarter. Revenue outside Americas increased by 22% to $159.1 million over the prior year’s quarter, or an 8% increase on a constant currency basis. Operating profit for the June quarter was $66.7 million and cash flow from operations was a robust $74.3 million, demonstrating excellent operating performance.”

The company also announced today the acquisition, on August 1st, of German-based Gründler GmbH, a developer of innovative medical humidification products. These humidifiers can be used with a wide range of ventilators, from neonatal and pediatric, to non-invasive pressure support, to those used in the intensive care unit. ResMed will retain Gründler’s existing staff and facilities, and the business will become part of ResMed’s newly-created Respiratory Care Strategic Business Unit. The transaction is not expected to have a material impact on ResMed’s financial results.

Dr. Farrell continued, “We not only had a strong quarter and year, but we have been active in the last few months with small technology-focused acquisitions and partnerships that will further our strategy to reach deeper into the vastly underpenetrated market for sleep-disordered breathing, as well as serve existing patients. In May, we informed you of our reorganization with the intention to be more aggressive in driving our key strategic initiatives and we have done just that. With the BiancaMed acquisition in July of this year, we can provide an innovative, convenient, non-contact device to monitor sleep and breathing in the home and hospital, while increasing our focus

on opportunities in chronic disease states related to sleep-disordered breathing, such as heart failure and chronic obstructive pulmonary disease. Our recently-announced partnership with CareFusion allows us to quickly establish a presence for Stellar 100 and 150 in the U.S. institutional healthcare market and creates an opportunity to enlarge our footprint in ventilation. Our acquisition of Gründler expands that footprint even further by adding high-quality humidification technology and products. We now have very competitive humidification solutions that provide superior therapy under a broad range of operating conditions. Due to the strong correlation between sleep-disordered breathing and comorbidities, such as heart disease and diabetes, chronic obstructive pulmonary disease, peri-operative death and occupational health and safety, we believe that there are significant opportunities to further penetrate the market; these recent acquisitions and partnership provide us with more options to achieve that goal.”

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 617-213-8059 (domestic) or +1 617-213-8059 (international) and entering conference pass code no. 96620149. 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. 93983593.

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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