Exhibit 32.1

                             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 Culp,  Inc. (the "Company") on
Form 10-Q for the period ended August 1, 2004 as filed with the  Securities  and
Exchange  Commission on the date hereof (the  "Report"),  I, Robert G. Culp,III,
Chairman of the Board and Chief  Executive  Officer of the  Company,  (principal
executive  officer)  certify,  pursuant to 18 U.S.C.  Section  1350,  as adopted
pursuant  to  Section  906  of  the  Sarbanes-Oxley  Act of  2002,  that,  to my
knowledge:

     (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 result of  operations of the
Company.


/s/ Robert G. Culp, III

Chairman of the Board and
Chief Executive Officer (principal executive officer)

September 10, 2004

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