EXHIBIT 32.1

 CERTIFICATION OF CHIEF EXECUTIVE OFFICER 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 Hillenbrand Industries, Inc. (the
"Company") on Form 10-Q for the period ending March 31, 2005 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I,
Frederick W. Rockwood, President and Chief Executive Officer of the Company,
certify, 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/ Frederick W. Rockwood
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Frederick W. Rockwood
President and Chief Executive Officer
May 9, 2005

A SIGNED ORIGINAL OF THIS WRITTEN STATEMENT REQUIRED BY SECTION 906 HAS BEEN
PROVIDED TO HILLENBRAND INDUSTRIES, INC. AND WILL BE RETAINED BY HILLENBRAND
INDUSTRIES, INC. AND FURNISHED TO THE SECURITIES AND EXCHANGE COMMISSION OR ITS
STAFF UPON REQUEST.