Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER ENDED AND NINE MONTHS ENDED MARCH 31, 2013

SAN DIEGO, April 25, 2013 – ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended March 31, 2013. Revenue for the quarter ended March 31, 2013 was $383.6 million, a 10% increase (also a 10% increase on a constant currency basis) over the quarter ended March 31, 2012. For the quarter ended March 31, 2013, net income was $84.9 million, an increase of 31% compared to the quarter ended March 31, 2012. Diluted earnings per share for the quarter ended March 31, 2013 were $0.58, an increase of 32% compared to the quarter ended March 31, 2012.

SG&A expenses were $109.6 million for the quarter ended March 31, 2013, an increase of $7.7 million, or 8% (also an 8% increase on a constant currency basis) compared to the quarter ended March 31, 2012. SG&A costs were 28.6% of revenue in the quarter ended March 31, 2013, compared to 29.2% for the quarter ended March 31, 2012.

R&D expenses were $31.2 million for the quarter ended March 31, 2013, an increase of $2.8 million, or 10% (an 11% increase on a constant currency basis) compared to the quarter ended March 31, 2012. R&D expenses were 8.1% of revenue in the quarter ended March 31, 2013, consistent with 8.1% for the quarter ended March 31, 2012.

The company amortized acquired intangibles of $2.5 million ($1.9 million, net of tax) during the quarter ended March 31, 2013. Stock-based compensation costs incurred during the quarter ended March 31, 2013 of $10.2 million ($7.2 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, 2013, revenue was $1.1 billion, an increase of 10% over the nine months ended March 31, 2012 (a 12% increase on a constant currency basis). For the nine months ended March 31, 2013, income from operations and net income were $268.7 million and $234.1 million, an increase of 31% and 32%, respectively, compared to the nine months ended March 31, 2012. Diluted earnings per share for the nine months ended March 31, 2013 were $1.60 per diluted share, an increase of 36% compared to the nine months ended March 31, 2012.

Inventory, at $166.5 million, decreased by $7.9 million compared to June 30, 2012. Accounts receivable days sales outstanding, at 67 days, decreased by 1 day compared to June 30, 2012.

Additionally, the Board of Directors has today declared a quarterly dividend of $0.17 per share, which will have a record date of May 21, 2013, and be payable on June 18, 2013. The dividend will be paid in U.S. currency to holders of ResMed’s common stock trading on the New York Stock Exchange (NYSE). Holders of CHESS Depositary Instruments (CDIs) trading on the Australian Securities 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. Because the two exchanges have different settlement and transfer procedures, the ex-dividend periods before the record date will be different for common stock and for CDIs. The ex-dividend date will be May 15, 2013 for CDI holders and May 17, 2013 for common stock holders. As a result of these differences, ResMed has received a waiver from the ASX’s settlement operating rules, which will allow ResMed to defer processing conversions between its common stock and CDI registers from May 15, 2013 through May 21, 2013, inclusive.

Michael “Mick” Farrell, chief executive officer, commented, “In the third quarter of fiscal 2013 we showed strong year-over-year growth on both top and bottom lines. Revenue in the Americas increased by 13%, to $215.2 million over the prior year’s quarter. Revenue outside the Americas was $168.4 million, an increase of 6% (also a 6% increase on a constant currency basis) over the prior year’s quarter. Operating profit for the March quarter was $96.1 million, cash flow from operations was $107.0 million, while gross margin was 62.4%, all demonstrating excellent operating performance. During the quarter, we also repurchased 1.5 million shares, at a cost of $67.3 million, as part of our ongoing capital management program.

“We are confident we have the right product pipeline for the future. We will be launching an important and exciting new mask this quarter, and expect to launch an additional mask later this calendar year. Finally, we are pleased to announce the launch of a new product today: VPAP™ COPD. The VPAP COPD is the first and only home bilevel cleared by the FDA specifically for the treatment of chronic obstructive pulmonary disease (COPD), giving patients and payors a weapon in the fight to keep COPD patients out of the hospital. We have also developed new ClimateLine^MAXTM Oxy tubing that connects between the humidifier and mask, with an oxygen line input next to the VPAP COPD device, enhancing comfort and ease of use. Both of these products will improve the lives of patients suffering from this debilitating and costly chronic disease.”

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 847-585-4405 (domestic) or +1 847-585-4405 (international) and entering conference passcode no. 34598681. 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 30 minutes after the live call and will be available for two weeks. A telephone replay of the conference call is available by dialing 630-652-3042 (domestic) and +1 630-652-3042 (international) and entering conference I.D. No. 34598681.

Further information can be obtained by contacting Constance Bienfait at ResMed Inc., San Diego, at (858) 836-5971; Brett Sandercock at ResMed Limited, Sydney, at (+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, new product launches, 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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