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 September 30, 2003 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
Terry L. Shepherd, Chief Executive Officer of the Company, certify, pursuant to
18 U.S.C. ss.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/ Terry L. Shepherd
                                        ------------------------------------
                                        Terry L. Shepherd
                                        Chairman and Chief Executive Officer
                                        November 11, 2003