Exhibit 99.1

ATWOOD OCEANICS ANNOUNCES DEPARTURE OF CHIEF FINANCIAL OFFICER

HOUSTON, May 27, 2015 — Atwood Oceanics, Inc. (NYSE: ATW) announced today that Mark L. Mey has resigned from his position as Executive Vice President and Chief Financial Officer of the Company to pursue other interests.

Rob Saltiel, President and Chief Executive Officer of Atwood, remarked, “Mark has played a significant role in the Company’s growth strategy over the past five years, and we are sorry to see him leave.”

The Board of Directors has appointed Mark W. Smith as Chief Financial Officer on an interim basis. Mr. Smith has served as Vice President, Chief Accounting Officer and Controller since May 2014 and in other finance roles since joining the Company in February 2009. Including his service to the Company, Mr. Smith has over 20 years’ experience in the financial, consulting and energy industries.

Atwood Oceanics, Inc. is a leading offshore drilling company engaged in the drilling and completion of exploration and development wells for the global oil and gas industry. The Company currently owns 12 mobile offshore drilling units and is constructing two ultra-deepwater drillships. The Company was founded in 1968 and is headquartered in Houston, Texas. Atwood Oceanics, Inc. common stock is traded on the New York Stock Exchange under the symbol “ATW.”

As part of our ongoing commitment to our shareholders, Atwood Oceanics uses a variety of Social Networks sites to disseminate company information. For a full list of the official Social Media pages for Atwood Oceanics, please visit the Social Media Disclaimer page of our IR site at: http://ir.atwd.com/GenPage.aspx?IID=4010374&GKP=210376.

Media Contact: Mark W. Smith

Interim CFO

281-749-7940