St. Jude Medical (STJ) 10-Q 2008 Q1 Quarterly report

EXHIBIT 32.1

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of St. Jude Medical, Inc. (the Company) on Form 10-Q for the period ended March 29, 2008 as filed with the Securities and Exchange Commission (the Report), I, Daniel J. Starks, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ DANIEL J. STARKS

Daniel J. Starks
Chairman, President and Chief Executive Officer
May 5, 2008