<PAGE>   1
                                                                     EXHIBIT 4.1


                                 FIRST AMENDMENT
                               TO CREDIT AGREEMENT


         This First Amendment to Credit Agreement (this "Amendment"), dated as
of February 16, 1999, is by and among Gaylord Container Corporation, a Delaware
corporation (the "Borrower"), the undersigned financial institutions in their
capacities as lenders (collectively, the "Lenders"), and Bankers Trust Company,
as agent (the "Agent") for the Lenders.

                              W I T N E S S E T H :

         WHEREAS, the Borrower, the Lenders and the Agent are parties to that
certain Credit Agreement dated as of June 19, 1998 (as amended, restated,
supplemented or otherwise modified and in effect from time to time, the "Credit
Agreement"), pursuant to which the Lenders have provided to the Borrower credit
facilities and other financial accommodations; and

         WHEREAS, the Borrower has requested that the Agent and the Lenders
amend the Credit Agreement in certain respects as set forth herein and the
Lenders and the Agent are agreeable to the same, subject to the terms and
conditions hereof;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants contained herein, and other good and valuable consideration the
receipt and adequacy of which are hereby acknowledged, the parties hereto hereby
agree as follows:

         1. Defined Terms. Terms capitalized herein and not otherwise defined
herein are used with the meanings ascribed to such terms in the Credit
Agreement.

         2. Amendments to Credit Agreement. The Credit Agreement is, as of the
Effective Date (as defined below), hereby amended as follows:

                  (a) Section 1.1 of the Credit Agreement is amended by deleting
the definitions of "Applicable Base Rate Margin" and "Applicable Eurodollar Rate
Margin" in their entirety and substituting therefor the following:

         "Applicable Base Rate Margin" means at any date, (i) with respect to
         Revolving Loans, the applicable percentage set forth in the following
         table under the column Applicable Base Rate Margin for Revolving Loans
         opposite the Most Recent Ratio of Total Debt to EBITDA as of such date
         and (ii) with respect to Term Loans, 2.25%:


<PAGE>   2




<TABLE>
<CAPTION>

                   ===========================================================================
                             MOST RECENT                           APPLICABLE BASE RATE
                         RATIO OF TOTAL DEBT                            MARGIN FOR
                              TO EBITDA                              REVOLVING LOANS
                   ===========================================================================
                   <S>                                                   <C>    

                   Less than 3.00 to 1.00                                 1.00%
                   ===========================================================================
                   Equal to or greater than 3.00 to 1.00
                   but less than 3.50 to 1.00                             1.25%
                   ===========================================================================
                   Equal to or greater than 3.50 to 1.00
                   but less than 4.00 to 1.00                             1.50%
                   ===========================================================================
                   Equal to or greater than 4.00 to 1.00
                   but less than 4.50 to 1.00                             1.75%
                   ===========================================================================
                   Equal to or greater than 4.50 to 1.00
                   but less than 5.00 to 1.00                             2.00%
                   ===========================================================================
                   Greater than or equal to 5.00 to 1.00
                                                                          2.25%
                   ===========================================================================
</TABLE>

         "Applicable Eurodollar Rate Margin" means at any date (i) with respect
         to Revolving Loans, the applicable percentage set forth in the
         following table under the column Applicable Eurodollar Rate Margin for
         Revolving Loans opposite the Most Recent Ratio of Total Debt to EBITDA
         as of such date and (ii) with respect to Term Loans, 3.25%:
<TABLE>
<CAPTION>

                  ============================================================================
                           MOST RECENT                         APPLICABLE EURODOLLAR RATE
                       RATIO OF TOTAL DEBT                     MARGIN FOR REVOLVING LOANS
                            TO EBITDA
                  ============================================================================
                  <S>                                                     <C>     
                  Less than 3.00 to 1.00                                  2.00%
                  ============================================================================
                  Equal to or greater than 3.00 to 1.00
                  but less than 3.50 to 1.00                              2.25%
                  ============================================================================
                  Equal to or greater than 3.50 to 1.00
                  but less than 4.00 to 1.00                              2.50%
                  ============================================================================
                  Equal to or greater than 4.00 to 1.00
                  but less than 4.50 to 1.00                              2.75%
                  ============================================================================
                  Equal to or greater than 4.50 to 1.00
                  but less than 5.00 to 1.00                              3.00%
                  ============================================================================
                  Greater than or equal to 5.00 to 1.00
                                                                          3.25%
                  ============================================================================
</TABLE>





                                       -2-


<PAGE>   3








                  (b) Section 1.1 of the Credit Agreement is further amended by
deleting the ratio "4.00 to 1.0" appearing in the definition of "Most Recent
Ratio of Total Debt to EBITDA " and substituting the ratio "5.00 to 1.00"
therefor.

                  (c) Section 9.2 of the Credit Agreement is amended by deleting
such Section in its entirety and substituting therefor the following:

         "9.2 Minimum Consolidated EBITDA . Permit the Consolidated EBITDA of
         Borrower and its Subsidiaries (a) to be less than (i) $14,000,000 for
         the one fiscal quarter ending September 30, 1998, (ii) $26,000,000 for
         the two fiscal quarter period ending December 31, 1998 and (iii)
         $28,000,000 for the three fiscal quarter period ending March 31, 1999,
         and (b) for the applicable Test Period ending on a date set forth below
         to be less than the amount set for the opposite such date:

                  Date                               Minimum Consolidated EBITDA

         June 30, 1999                                        $37,000,000
         September 30, 1999                                   $47,000,000
         December 31, 1999                                    $58,000,000
         March 31, 2000                                       $88,000,000
         June 30, 2000                                        $110,000,000
         September 30, 2000                                   $135,000,000
         December 31, 2000 and
         each fiscal quarter thereafter                       $150,000,000

         provided, however, that if Borrower and its Subsidiaries fail to
         maintain Consolidated EBITDA of at least $47,000,000 for the Test
         Period ending September 30, 1999, Borrower shall be allowed to satisfy
         the minimum Consolidated EBITDA requirement under this Section 9.2 for
         such Test Period by maintaining Consolidated EBITDA of Borrower and its
         Subsidiaries of not less than $10,000,000 for the one fiscal quarter
         ending September 30, 1999."

                  (d) Section 9.3 of the Credit Agreement is hereby amended by
deleting such Section in its entirety and substituting therefor the following:

         "9.3 Interest Coverage Ratio. Permit the Interest Coverage Ratio (a) to
         be less than (i) 0.60 to 1.00 for the one fiscal quarter ending
         September 30, 1998, (ii) 0.65 to 1.00 for the two fiscal quarter period
         ending December 31, 1998 and (iii) .45 to 1.00 for the three fiscal
         quarter period ending March 31, 1999, and (b) for the applicable Test
         Period ending on a date set forth below to be less than the ratio set
         forth opposite such date:

                                       -3-



<PAGE>   4


<TABLE>
<CAPTION>



                  Date                                                 Ratio
                  <S>                                                  <C>    

                  June 30, 1999                                        0.45 to 1.00
                  September 30, 1999                                   0.55 to 1.00
                  December 31, 1999                                    0.65 to 1.00
                  March 31, 2000                                       1.00 to 1.00
                  June 30, 2000                                        1.25 to 1.00
                  September 30, 2000                                   1.50 to 1.00
                  December 31, 2000                                    2.00 to 1.00
                  March 31, 2001 and
                  each fiscal quarter thereafter                       2.50 to 1.00
</TABLE>

                  provided, however, that if Borrower and its Subsidiaries fail
                  to maintain an Interest Coverage Ratio of at least 0.55 to
                  1.00 for the Test Period ending September 30, 1999, Borrower
                  shall be allowed to satisfy the minimum Interest Coverage
                  Ratio requirement under this Section 9.3 for such Test Period
                  by maintaining an Interest Coverage Ratio of not less than
                  0.55 to 1.00 for the one fiscal quarter ending September 30,
                  1999."

         3. Amendment Fee. In consideration of the execution of this Amendment
by the Agent and the Lenders, the Borrower hereby agrees to pay each Lender
which executes this Amendment on or prior to February 4, 1999 a fee (the
"Amendment Fee") in an amount equal to such Lender's Commitment multiplied by
0.25%.

         4. Borrower's Representations and Warranties. In order to induce the
Agent and the Lenders to enter into this Amendment, the Borrower hereby
represents and warrants to the Agent and the Lenders as follows:

                           (i) The Borrower has the right, power and capacity
                  and has been duly authorized and empowered by all requisite
                  corporate and shareholder action to enter into, execute,
                  deliver and perform this Amendment and all agreements,
                  documents and instruments executed and delivered pursuant to
                  this Amendment.

                           (ii) This Amendment constitutes the Borrower's legal,
                  valid and binding obligation, enforceable against it, except
                  as enforcement thereof may be subject to the effect of any
                  applicable bankruptcy, insolvency, reorganization, moratorium
                  or similar laws affecting creditors' rights generally and
                  general principles of equity (regardless of whether such
                  enforcement is sought in a proceeding in equity or at law or
                  otherwise).

                           (iii) After giving effect to the amendments
                  contemplated by this Amendment, the representations and
                  warranties contained in the Credit Agreement and the other
                  Loan Documents are true and correct in all material
                                       -4-



<PAGE>   5




                  respects at and as of the Effective Date as though made on and
                  as of the Effective Date (except to the extent specifically
                  made with regard to a particular date, in which case such
                  representation and warranty is true and correct in all
                  material respects as of such earlier date).

                           (iv) The Borrower's execution, delivery and
                  performance of this Amendment do not and will not violate its
                  Certificate of Incorporation or By-laws, any law, rule,
                  regulation, order, writ, judgment, decree or award applicable
                  to it or any contractual provision to which it is a party or
                  to which it or any of its property is subject.

                           (v) No authorization or approval or other action by,
                  and no notice to or filing or registration with, any
                  governmental authority or regulatory body (other than those
                  which have been obtained and are in force and effect) is
                  required in connection with its execution, delivery and
                  performance of this Amendment and all agreements, documents
                  and instruments executed and delivered pursuant to this
                  Amendment.

                           (vi) After giving effect to the amendments
                  contemplated by this Amendment, no Event of Default or
                  Unmatured Event of Default exists under the Credit Agreement
                  or would exist after giving effect to the transactions
                  contemplated by this Amendment.

         5. Conditions to Effectiveness of Amendment. This Amendment shall
become effective on the date (the "Effective Date") each of the following
conditions precedent is satisfied:

                  (a) Execution and Delivery. The Borrower, the Agent, and the
Required Lenders shall have executed and delivered this Amendment.

                  (b) No Defaults. No Unmatured Event of Default or Event of
Default under the Credit Agreement (as amended hereby) shall have occurred and
be continuing.

                  (c) Representations and Warranties. After giving effect to the
amendments contemplated by this Amendment, the representations and warranties of
the Borrower contained in this Amendment, the Credit Agreement and the other
Loan Documents shall be true and correct in all material respects as of the
Effective Date, with the same effect as though made on such date, except to the
extent that any such representation or warranty relates to an earlier date, in
which case such representation or warranty shall be true and correct in all
material respects as of such earlier date.

                  (d) Payment of Amendment Fee. The Borrower shall have paid in
full to the Agent, for ratable distribution to those Lenders that have signed
this Amendment on or prior to February 4, 1999, an amount equal to the
Amendment Fee on or prior to February 5, 1999; provided, however, that the
Amendment Fee shall be payable only in the event that this Amendment has been
executed by the Agent and the Required Lenders.
                                       -5-



<PAGE>   6





                  (e) Officer's Certificate. The Borrower shall have duly
executed and delivered to the Agent a certificate of a Responsible Officer of
the Borrower dated as of the Effective Date in the form of Exhibit A attached
hereto.

         6. Miscellaneous. The parties hereto hereby further agree as follows:

                  (a) Costs, Expenses and Taxes. The Borrower hereby agrees to
pay all reasonable fees, costs and expenses of the Agent incurred in connection
with the negotiation, preparation and execution of this Amendment and the
transactions contemplated hereby, including, without limitation, the reasonable
fees and expenses of Winston & Strawn, counsel to the Agent.

                  (b) Counterparts. This Amendment may be executed in one or
more counterparts, each of which, when executed and delivered, shall be deemed
to be an original and all of which counterparts, taken together, shall
constitute but one and the same document with the same force and effect as if
the signatures of all of the parties were on a single counterpart, and it shall
not be necessary in making proof of this Amendment to produce more than one (1)
such counterpart.

                  (c) Headings. Headings used in this Amendment are for
convenience of reference only and shall not affect the construction of this
Amendment.

                  (d) Integration. This Amendment and the Credit Agreement (as
amended hereby) constitute the entire agreement among the parties hereto with
respect to the subject matter hereof.

                  (e) Governing Law. THIS AMENDMENT SHALL BE GOVERNED BY, AND
CONSTRUED AND ENFORCED IN ACCORDANCE WITH, THE INTERNAL LAWS AND DECISIONS OF
THE STATE OF NEW YORK (WITHOUT REFERENCE TO CONFLICT OF LAWS PRINCIPLES).

                  (f) Binding Effect. This Amendment shall be binding upon and
inure to the benefit of and be enforceable by the Borrower, the Agent and the
Lenders and their respective successors and assigns. Except as expressly set
forth to the contrary herein, this Amendment shall not be construed so as to
confer any right or benefit upon any Person other than the Borrower, the Agent
and the Lenders and their respective successors and permitted assigns.

                  (g) Amendment; Waiver. The parties hereto agree and
acknowledge that nothing contained in this Amendment in any manner or respect
limits or terminates any of the provisions of the Credit Agreement or any of the
other Loan Documents other than as expressly set forth herein and further agree
and acknowledge that the Credit Agreement (as amended hereby) and each of the
other Loan Documents remain and continue in full force and effect and are hereby
ratified and confirmed. Except to the extent expressly set forth herein, the
execution, delivery and effectiveness of this Amendment shall not operate as a
waiver of any rights, power or remedy of the Lenders or the Agent under the
Credit Agreement or any other Loan Document,
                                       -6-



<PAGE>   7




nor constitute a waiver of any provision of the Credit Agreement or any other
Loan Document. No delay on the part of any Lender or the Agent in exercising any
of their respective rights, remedies, powers and privileges under the Credit
Agreement or any of the Loan Documents or partial or single exercise thereof,
shall constitute a waiver thereof. None of the terms and conditions of this
Amendment may be changed, waived, modified or varied in any manner, whatsoever,
except in accordance with Section 12.1 of the Credit Agreement.

                            [signature pages follow]




































                                       -7-


<PAGE>   8




                        
         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed by their respective officers thereunto duly authorized, as of the date
first written above.

                              GAYLORD CONTAINER CORPORATION

                              By:
                                    ------------------------------------
                              Name: /s/ Thomas M. Steffen               
                                    ------------------------------------
                              Title:  Assistant Treasurer               
                                    ------------------------------------
                                                                        
                              BANKERS TRUST COMPANY, in its individual  
                                      capacity and as Agent             
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Robert R. Telesca               
                                    ------------------------------------
                              Title:  Assistant Vice President          
                                    ------------------------------------
                                                                        
                              THE BANK OF NEW YORK                      
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Richard A. Raffetto          
                                    ------------------------------------
                              Title:   Vice President                   
                                    ------------------------------------
                                                                        
                              NATIONSBANK, N.A.                         
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Michael L. Short             
                                    ------------------------------------
                              Title:   Senior Vice President            
                                    ------------------------------------
                                                                        
                              CHRISTIANIA BANK                          
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Carl Petter Svenosen         
                                    ------------------------------------
                              Title:   Senior Vice President            
                                    ------------------------------------
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Peter M. Dodge               
                                    ------------------------------------
                              Title:   Senior Vice President            
                                    ------------------------------------
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
                          Gaylord Container Corporation                 
                       First Amendment to Credit Agreement              
                                                                        
<PAGE>   9
                                                                        
                                                                        
                                                                        
                                                                        
                              TORONTO DOMINION [TEXAS], INC.            
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Shelia M. Conley             
                                    ------------------------------------
                              Title:   Vice President                   
                                    ------------------------------------
                                                                        
                              SANWA BUSINESS CREDIT CORPORATION         
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Peter L. Skavia              
                                    ------------------------------------
                              Title:   Vice President                   
                                    ------------------------------------
                                                                        
                              TRANSAMERICA BUSINESS CREDIT              
                                   CORPORATION                          
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Perry Vavoules               
                                    ------------------------------------
                              Title:   Senior Vice President            
                                    ------------------------------------
                                                                        
                              BANKBOSTON, N.A.                          
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Rennee A. Ross               
                                    ------------------------------------
                              Title:                                    
                                    ------------------------------------
                                                                        
                              PILGRIM PRIME RATE TRUST                  
                              By: Pilgrim Investment, Inc., as its      
                              Investment Advisor                        
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ Michel Prince, CFA           
                                    ------------------------------------
                              Title:   Vice President                   
                                    ------------------------------------
                                                                        
                                                                        
                                                                        
                                                                        
                          Gaylord Container Corporation                 
                       First Amendment to Credit Agreement              
                                                                        
                                                                        
<PAGE>   10
                                                                        
                                                                        
                                                                        
                             ML CLO XV PILGRIM AMERICA                 
                                 (CAYMAN) LTD.                         
                             By: Pilgrim Investment, Inc., as its      
                               Investment Advisor                      
                                                                       
                             By:                                       
                                   -------------------------------------
                             Name: /s/ Michel Prince, CFA              
                                   -------------------------------------
                             Title:   Vice President                   
                                   -------------------------------------
                                                                       
                             STEIN ROE & FARNHAM INCORPORATED,         
                                   as agent for Keyport Life Insurance Company
                                                                       
                             By:                                       
                                   -------------------------------------
                             Name: /s/ Brian W. Good                
                                   -------------------------------------
                             Title:   Vice President & Portfolio Manager
                                   -------------------------------------
                                                                       
                             SENIOR DEBT PORTFOLIO                     
                             By: Boston Management and Research,       
                                   as Investment Advisor               
                                                                       
                             By:                                       
                                   -------------------------------------
                             Name: /s/ Payson F. Swaffield          
                                   -------------------------------------
                             Title:   Vice President                   
                                   -------------------------------------
                                                                       
                             BEAR STEARNS INVESTMENT PRODUCTS, INC.    
                                                                       
                             By:                                       
                                   -------------------------------------
                             Name: /s/ Harry Rosenberg              
                                   -------------------------------------
                             Title:   Authorized Signatory             
                                   -------------------------------------
                                                                       
                             KZH PAMCO LLC                             
                                                                       
                             By:                                       
                                   -------------------------------------
                             Name: /s/ Virginia Conway              
                                   -------------------------------------
                             Title:   Authorized Agent                 
                                   -------------------------------------
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
                         Gaylord Container Corporation                 
                      First Amendment to Credit Agreement              
                                                                       
                                                                       
<PAGE>   11
                                                                        
                                                                        
                                                                        
                              CERES FINANCE LTD.                        
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ John H. Cullinane            
                                    ------------------------------------
                              Title:   Director                         
                                    ------------------------------------
                                                                        
                              STRATA FUNDING LTD.                       
                                                                        
                              By:                                       
                                    ------------------------------------
                              Name: /s/ John H. Cullinane            
                                    ------------------------------------
                              Title:   Director                         
                                    ------------------------------------


                          Gaylord Container Corporation
                       First Amendment to Credit Agreement
<PAGE>   12






                              BLACK DIAMOND CLO 1998-1 LTD.
                              By: Black Diamond Capital Management, L.L.C.,
                              as Collateral Manager

                              By:
                                    ------------------------------------
                              Name: /s/ James J. Zenni Jr.
                                    ------------------------------------
                              Title:   President/Principal              
                                    ------------------------------------






                          Gaylord Container Corporation
                       First Amendment to Credit Agreement



<PAGE>   13


                                  EXHIBIT A

                            OFFICER'S CERTIFICATE


                  The undersigned, Thomas M. Steffen, hereby certifies that he
is the duly elected Assistant Treasurer of Gaylord Container Corporation, a
Delaware corporation (the "Borrower"), and pursuant to that certain First
Amendment to Credit Agreement dated as of February 16, 1999 (the Amendment") by
and among the Borrower, Bankers Trust Company, as Agent, and the financial
institutions party thereto as lenders (capitalized terms used herein shall,
unless otherwise defined herein, have the meaning provided in the Amendment),
hereby further certifies as follows:

                  1. No Unmatured Event of Default or Event of Default under the
Credit Agreement (as amended by the Amendment) has occurred and is continuing as
of the date hereof.

                  2. After giving effect to the amendments contemplated by the
Amendment, the representations and warranties of the Borrower contained in the
Amendment, the Credit Agreement and the other Loan Documents are true and
correct in all material respects as of the date hereof, with the same effect as
though made on such date, except to the extent that any such representation or
warranty relates to an earlier date, in which case such representation or
warranty is true and correct in all material respects as of such earlier date.

                  IN WITNESS WHEREOF, the undersigned has caused this
Certificate to be duly executed and delivered as of February 16, 1999.



                                                  GAYLORD CONTAINER CORPORATION
                                                        

                                                  By: 
                                                     ---------------------------
                                                     Thomas M. Steffen
                                                     Assistant Treasurer




                         Gaylord Container Corporation
                      First Amendment to Credit Agreement