Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND NINE MONTHS ENDED MARCH 31, 2010

SAN DIEGO, California, April 29, 2010 - ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended March 31, 2010. Revenue for the quarter ended March 31, 2010 was $278.7 million, a 22% increase (an 18% increase on a constant currency basis) over the quarter ended March 31, 2009. For the quarter ended March 31, 2010, income from operations was $61.2 million and net income was $48.8 million, an increase of 16% and 25%, respectively, compared to the quarter ended March 31, 2009. Diluted earnings per share for the quarter ended March 31, 2010 were $0.63, an increase of 24% compared to the quarter ended March 31, 2009.

SG&A expenses were $84.1 million for the quarter ended March 31, 2010, an increase of $13.3 million, or 19% (an 11% increase on a constant currency basis) over the quarter ended March 31, 2009. SG&A expenses were negatively impacted by the depreciation of the U.S. dollar against international currencies. The increase in SG&A was primarily due to expenses necessary to support sales growth. SG&A costs were 30% of revenue in the quarter ended March 31, 2010, compared to 31% in the quarter ended March 31, 2009.

R&D expenses were $18.3 million for the quarter ended March 31, 2010, or 7% of revenue. R&D expenses increased by 32% (a 4% increase on a constant currency basis) compared to the quarter ended March 31, 2009. R&D expenses were negatively impacted by the depreciation of the U.S. dollar against international currencies, particularly the Australian dollar.

The company amortized acquired intangibles of $2.0 million ($1.3 million, net of tax) during the quarter ended March 31, 2010. Stock-based compensation costs incurred during the quarter ended March 31, 2010 of $8.0 million ($5.7 million, net of tax) consisted of expenses associated with stock options, and restricted stock units, and our employee stock purchase plan.

During the quarter ended March 31, 2010, the company donated $1.0 million ($0.6 million, net of tax) to the ResMed Foundation. The Foundation’s primary mission is to promote research, as well as public and physician awareness of the importance of sleep and respiratory health throughout the world.

For the nine months ended March 31, 2010, revenue was $800.8 million, an increase of 20% over the nine months ended March 31, 2009. For the nine months ended March 31, 2010, income from operations and net income were $171.8 million and $136.9 million, an increase of 30% and 35%, respectively, compared to the nine months ended March 31, 2009. Diluted earnings per share for the nine months ended March 31, 2010 were $1.77 per diluted share, an increase of 35% compared to the nine months ended March 31, 2009.

Inventory, at $197.8 million, increased by $40.4 million compared to June 30, 2009. Accounts receivable days sales outstanding, at 70 days, decreased by 4 days compared to June 30, 2009.

Kieran T. Gallahue, President and Chief Executive Officer, commented, “In the third quarter of fiscal 2010, we continued to show strong growth year-over-year in the Americas, as well as in Europe and Asia/Pacific. Our favorable mix of product sales and market share gains led to a 20% increase in the Americas over the prior year’s quarter, resulting in $146.8 million in revenue. Sales outside the Americas increased by 25% to $131.9 million over the prior year’s quarter, or a 16% increase on a constant currency basis. Operating profit for the March quarter was $61.1 million and cash flow from operations was $53.5 million, demonstrating excellent operating performance. The launches of the S9™ AutoSet and Elite products, the Swift™ FX mask and the Mirage™ SoftGel mask are going especially well. The two new masks are receiving outstanding feedback from customers and patients. HME dealers, physicians, and patients are excited about the improved comfort and sleek, bedroom-friendly design of the S9, but most importantly about the potential for the S9 Series to drive greater patient adherence to therapy.

“Our opportunities for sustained growth continue to present themselves with the increasing confirmation of the strong impact of the relationship between sleep-disordered breathing, obstructive sleep apnea and co-morbidities such as cardiac disease, diabetes, hypertension and obesity. The National Institutes of Health released a clinical study just this month showing that obstructive sleep apnea is associated with an increased risk of stroke in middle-aged and older adults, especially men. There continues to be abundant new evidence that treating sleep-disordered breathing and obstructive sleep apnea can improve health, quality of life and also mitigate the dangers of sleep apnea in occupational health and safety, especially in the transport industry.”

About ResMed

ResMed is a leading developer, manufacturer and distributor of medical equipment for treating, diagnosing, and managing sleep-disordered breathing and other respiratory disorders. 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 (800) 573-4754 (domestic) or +1 (617) 224-4325 (international) and entering conference I.D. No. 85590553. Please allow extra time prior to the call to visit the Web 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) and +1 (617) 801-6888 (international) and entering conference I.D. No. 23407392.

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 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 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 Web site.

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RESMED INC AND SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

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RESMED INC AND SUBSIDIARIES

Consolidated Balance Sheets (Unaudited)

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

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