Accuray (ARAY) 10-Q 2010 Q3 Quarterly report

Exhibit 32.1

Certification of Chief Executive Officer and Chief Financial Officer

Pursuant to 18 U.S.C. § 1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officers of Accuray Incorporated, a Delaware corporation (the “Company”) hereby certifies, to such officers’ knowledge, that:

(i)     the accompanying Quarterly Report on Form 10-Q of the Company for the three and nine months ended March 31, 2010 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii)    the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: May 6, 2010

/s/ Euan S. Thomson

Euan S. Thomson, Ph.D.

President and Chief Executive Officer

/s/ Derek Bertocci

Derek Bertocci

Senior Vice President and Chief Financial Officer