EXHIBIT 32.1

                                  AMSURG CORP.

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of AmSurg Corp. (the "Company") on Form
10-Q for the period ending March 31, 2004, as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), each of the undersigned
certifies, pursuant to 18 U.S.C. Section 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/ Ken P. McDonald
                                          ------------------------------------
                                          Ken P. McDonald
                                          President and Chief Executive
                                          Officer of the Company

                                          May 7, 2004

                                          /s/ Claire M. Gulmi
                                          ------------------------------------
                                          Claire M. Gulmi
                                          Senior Vice President,
                                          Chief Financial
                                          Officer and Secretary
                                          of the Company

                                          May 7, 2004