EXHIBIT 32.1

                       CERTIFICATION FURNISHED 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 Pliant Corporation (the "Company") on
Form  10-Q for the  fiscal  quarter  ended  June  30,  2004,  as filed  with the
Securities and Exchange Commission on the date hereof (the "Report"),  I, Harold
C. Bevis, 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 to the best of 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 results of operations of the Company for
and as of the end of the periods covered in this Report.

/s/ Harold C. Bevis
-------------------------------------
Harold C. Bevis
Chief Executive Officer
August 5, 2004