EXHIBIT 32

                           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 Annual Report of Graham Corporation (the "Company") on
Form 10-K for the fiscal year ended 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.

<Table>
                                                 
             /s/ ALVARO CADENA                                 /s/ J. RONALD HANSEN
- -------------------------------------------         -------------------------------------------
               Alvaro Cadena                                     J. Ronald Hansen
   President and Chief Executive Officer                      Chief Financial Officer
               June 18, 2004                                       June 18, 2004
</Table>

A signed original of this written statement required by Section 906 or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in the typed form within the electronic version of this written
statement required by Section 906, has been provided to Graham Corporation and
will be retained by Graham Corporation and furnished to the Securities and
Exchange Commission or its staff upon request.