Accuray (ARAY) 10-Q 2008 Q3 Quarterly report

Exhibit 32.1

Certification of Chief Executive Officer

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

(i)            the accompanying Quarterly Report on Form 10-Q of the Company for the three months ended March 29, 2008 (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 12, 2008

  /s/ Euan S. Thomson

Euan S. Thomson

Chief Executive Officer and
President