
<PAGE>
 
                                                                   Exhibit 10.40

                           FIFTH SUPPLEMENT INDENTURE

     FIFTH SUPPLEMENTAL INDENTURE (the "Supplemental Indenture"), dated as of
June 19, 1997, between Polymer Group, Inc., a Delaware corporation (the
"Company"), and Harris Trust and Savings Bank, an Illinois banking corporation
(the "Trustee").  All capitalized terms used herein without definition herein
shall have the meaning ascribed thereto in the Indenture (as defined).

                              W I T N E S S E T H:

     WHEREAS, pursuant to the Offer to Purchase and Consent Solicitation
Statement dated June 5, 1997 (the "Statement") and related Consent and Letter of
Transmittal (together with the Statement, the "Offer"), the Corporation has
commenced an offer to purchase (the "Tender Offer") all of the Corporation's
outstanding 12 1/4% Senior Notes due 2002 (the "Notes") and to solicit consents
(the "Consent Solicitation") to the amendment of certain provisions of the
indenture, dated as of June 24, 1994, between the Company and First Union
National Bank of South Carolina ("First Union"), as amended by the First
Supplemental Indenture dated as of March 15, 1995 between the Company and First
Union, the Second Supplemental Indenture dated as of  September 14, 1995 among
the Company, First Union and Harris Trust and Savings Bank, as Trustee, the
Third Supplemental Indenture dated as of April 9, 1996 between the Company and
the Trustee, and the Fourth Supplemental Indenture dated as of August 14, 1996
between the Company and the Trustee (as so amended, the "Indenture"), pursuant
to which the Notes were issued;

     WHEREAS, Section 902 of the Indenture authorizes the Company and the
Trustee, from time to time, with the consent of the Holders of not less than a
majority in principal amount of Outstanding Notes and when authorized by a Board
Resolution, to amend the Indenture by supplemental indenture for the purpose
therein set forth;

     WHEREAS, in accordance with Section 902 of the Indenture, the Trustee, the
Company and the Holders (as defined in the Indenture) of a majority in principal
amount of the Outstanding Securities (as defined in the Indenture) as of the
date hereof have agreed to amend certain terms related to limitations on
Indebtedness (as set forth in Section 1011 of the Indenture), limitations on
Restricted Payments (as set forth in Section 1012 of the Indenture), limitations
on transactions with Affiliates (as set forth in Section 1013 of the Indenture),
limitations on certain Subordinated Indebtedness (as set forth in Section 1014
of the Indenture), limitations on Liens (as set forth in Section 1015 of the
Indenture), limitations on Restricted Subsidiary Capital Stock (as set forth in
Section 1018 of the Indenture), and limitations on Dividends and other payment
restrictions affecting Restricted Subsidiaries (as set forth in Section 1019 of
the Indenture);


<PAGE>
 
     WHEREAS, the Company and the Guarantors, by appropriate corporate action,
have determined to amend the provisions of the Indenture in the manner described
below and have taken all acts and proceedings required by law, by the Indenture,
and by their respective Articles of Incorporation and Bylaws necessary to duly
authorize, execute and deliver this Supplemental Indenture and to constitute
this Supplemental Indenture a legal, valid and binding agreement of the Company
and the Guarantors enforceable against the Company and Guarantors in accordance
with the terms herein;

     WHEREAS, the Company desires that the modifications, additions and
amendments contained herein become operative and effective on the date the
Company accepts for purchase and payment Notes validly tendered (and not validly
withdrawn) pursuant to the terms of the Offer.

     NOW, THEREFORE, the parties hereto agree as follows:

     Section 1.  Amendment to Section 101.  The text of Section 101 of the
Indenture is hereby amended as follows:

     Insert the following as a new definition immediately prior to the
definition of "Acquired Indebtedness":

          "Acceptance Date" means the date the Company accepts for purchase and
     payment Notes validly tendered (and not withdrawn) pursuant to the terms of
     the Offer to Purchase and Consent Solicitation Statement dated June 5,
     1997.

     Section 2.1    Amendments of Section 1011.  Section 1011 is hereby amended
by deleting the existing subsection in its entirety.

     Section 2.2    Amendments of Section 1012.  Section 1012 is hereby amended
by deleting the existing subsection in its entirety.

     Section 2.3    Amendments of Section 1013.  Section 1013 is hereby amended
by deleting the existing subsection in its entirety.

     Section 2.4    Amendments of Section 1014.  Section 1014 is hereby amended
by deleting the existing subsection in its entirety.

     Section 2.5    Amendments of Section 1015.  Section 1015 is hereby amended
by deleting the existing subsection in its entirety.

     Section 2.6    Amendments of Section 1018.  Section 1018 is hereby amended
by deleting the existing subsection in its entirety.

                                      -2-
<PAGE>
 
     Section 2.7    Amendments of Section 1019.  Section 1019 is hereby amended
by deleting the existing subsection in its entirety.

     Section 2.8    Deletion of Certain Definitions.  The Indenture is hereby
amended to delete all definitions and defined terms from the Indenture where all
references to such definitions or defined terms would be eliminated as a result
of the amendments set forth herein.

     Section 3.     Operative Effect of Amendments. Sections 2.1 through 2.8
shall not become operative unless and until the Company accepts for purchase and
payment Notes validly tendered (and not withdrawn) on the Acceptance Date
pursuant to the Offer, at which time such Sections shall become operative and
shall be in full force and effect.  In the event the Acceptance Dates does not
occur on or prior to October 1, 1997, such Sections shall be null and void and
of no further effect.

     Section 4.     Governing Law.  This Supplemental Indenture shall be
governed by and construed in accordance with the laws of the State of New York
applicable to contracts to be performed entirely in that State.

     Section 5.     Counterparts.  This Supplemental Indenture may be signed in
any number of counterparts, each of which shall be an original, with the same
effect as if the signatures thereto and hereto were upon the same instrument.

     Section 6.     Severability.  In case any provision in this Supplemental
Indenture shall be invalid, illegal or unenforceable, the validity, legality and
enforceability of the remaining provisions shall not in any way be affected or
impaired thereby.

     Section 7.     Ratification.  Except as expressly amended hereby, each
provision of the Indenture shall remain in full force and effect and, as amended
hereby, the Indenture is in all respects agreed to, ratified and confirmed by
each of the Company, the Guarantors and the Trustee.


                           *            *            *

                                      -3-
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the date first above written.

                                         POLYMER GROUP, INC.


                                         By:     /s/ Jerry Zucker
                                                 -------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer
                                         PGI POLYMER, INC.,
                                          as Guarantor


                                         By:     /s/ Jerry Zucker
                                                 -------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer
                                         FIBERTECH GROUP, INC.,
                                          as Guarantor


                                         By:     /s/ Jerry Zucker
                                         ---------------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer
                                         TECHNETICS GROUP, INC.,
                                          as Guarantor


                                         By:     /s/ Jerry Zucker
                                         ---------------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer

                                      -4-
<PAGE>
 
                             [Signatures Continued]



                                         FIBERGOL CORPORATION,
                                          as Guarantor


                                         By:     /s/ Jerry Zucker
                                         ---------------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer

                                         CHICOPEE HOLDINGS, INC.,
                                          as Guarantor


                                         By:     /s/ Jerry Zucker
                                         ---------------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer

                                         CHICOPEE, INC.,
                                          as Guarantor


                                         By:     /s/ Jerry Zucker
                                         ---------------------------------------
                                         Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer

                                      -5-
<PAGE>
 
                                 [Signatures Continued]


                                        PNA CORP.


                                        By:     /s/ Jerry Zucker
                                        ----------------------------------------
                                        Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer

                                        FNA POLYMER CORP.


                                        By:     /s/ Jerry Zucker
                                        ----------------------------------------
                                        Title:  Chairman, President & CEO

Attest:  /s/ James G. Boyd
         --------------------------------
         Title:  Executive Vice President
                 & Treasurer

                                        HARRIS TRUST AND SAVINGS BANK


                                        By:      /s/ Judy Bartolini
                                        ----------------------------------------
                                        Title:   Vice President

Attest:  /s/ D.G. Donovan
         -------------------------------
         Title:  Assistant Secretary

                                      -6-
