<PAGE>
 
                                                                    EXHIBIT 10.1

                                THIRD AMENDMENT
                                    TO THE
                               CREDIT AGREEMENT

                          Dated as of April 27, 1999


     This THIRD AMENDMENT dated as of April 27, 1999 (this "Third Amendment") is
between CORE, INC., a Massachusetts corporation (the "Borrower"), and FLEET
NATIONAL BANK, a national banking association (the "Bank").

     PRELIMINARY STATEMENTS.  The Borrower and the Bank entered into a Credit
Agreement dated as of August 31, 1998, which Credit Agreement was amended by a
First Amendment to the Credit Agreement dated as of December 31, 1998 and a
Second Amendment to the Credit Agreement dated as of February 19, 1999 (as so
amended, the "Credit Agreement").  The present maximum Commitment under the
Credit Agreement is $16,000,000 as a result of scheduled Commitment reductions
prior to the date hereof.  The Borrower has now requested that the Bank amend
the Credit Agreement to increase the maximum Commitment to $18,500,000, subject
to a revised schedule of mandatory Commitment reductions.  The Bank has agreed
to such request upon certain terms and conditions.

     NOW, THEREFORE, for valuable consideration, receipt of which is hereby
acknowledged, the Borrower and the Bank agree as follows:

     Section 1.  Amendments to the Credit Agreement.  Effective as of the
                 ----------------------------------                      
effective date hereof and subject to the satisfaction of the conditions
precedent set forth in Section 2 hereof, the Credit Agreement is amended as
follows:

     (a)  Section 1.1 (Definitions) is amended as follows:
          -------------------------                       

          (i)    the defined term "Anniversary Date" is deleted;

          (ii)   the defined term "Capital Expenditures" is deleted and replaced
                 with the following:

                 ""Capital Expenditures" means, for any period, the Dollar
                 amount of gross expenditures (including the principal portion
                 of rental payments in respect of Capital Lease Obligations)
                 made for fixed assets (including without limitation
                 expenditures for software development), real property, plant
                 and equipment, and all renewals, improvements and replacements
                 thereto (but not repairs thereof)
<PAGE>
 
                 incurred during such period, all as determined in accordance
                 with GAAP;"

          (iii)  the defined term "Registration Rights Agreement" is deleted and
                 replaced with the following"

                 ""Registration Rights Agreement" means each of (x) the
                 Registration Rights Agreement, in the form of Exhibit K hereto,
                                                               ---------
                 duly executed by the Borrower, and (y) the Registration
                 Rights Agreement in the form of Exhibit C to the Third
                                                 ---------
                 Amendment to the Credit Agreement dated as of April 27, 1999,
                 duly executed by the Borrower, in each case as the same may be
                 amended, supplemented, restated or otherwise modified and in
                 effect from time to time."

          (iv)   the defined term "Revolving Loan Termination Date" is deleted
                 and replaced with the following:

                 ""Revolving Loan Termination Date" means June 30, 2004."

          (v)    the defined term "Warrant" is deleted and replaced with the
                 following:

                 ""Warrant" means each of (x) the Warrant, in the form of
                 Exhibit J hereto, pursuant to which the Borrower grants to the
                 ---------
                 Bank warrants to purchase shares of the Common Stock of the
                 Borrower equal to 2% of the Borrower's outstanding Common
                 Stock, and (y) the Warrant, in the form of Exhibit B to the
                                                            ---------
                 Third Amendment to the Credit Agreement dated as of April 27,
                 1999, pursuant to which the Borrower grants to the Bank
                 warrants to purchase 187,000 shares of Common Stock of the
                 Borrower."

     (b)  Section 2.1 (The Revolving Loans) is amended by deleting the first
          ---------------------------------                                 
     sentence thereof and replacing it with the following:

          "Subject to the terms and conditions of this Agreement, the Bank
          agrees to make revolving loans to the Borrower (hereinafter
          collectively referred to as the "Revolving Loan" or "Revolving Loans")
          from time to time from and including the date hereof until the earlier
          of the Revolving Loan Termination Date or the termination of the
          Commitment of the Bank, up to, but not exceeding in the aggregate
          principal amount at any one time 
<PAGE>
 
                                      -3-



          outstanding, the amount of EIGHTEEN MILLION FIVE HUNDRED THOUSAND 
          DOLLARS ($18,500,000)."

     (c)  Subsection (a) of Section 2.5 (Mandatory Reduction of Commitment) is
          -----------------------------------------------------------------   
     deleted and replaced with the following:

          "(a)  On each of the dates indicated below, the Commitment of the Bank
          shall be reduced automatically in the following amounts:


--------------------------------------------------------------------
                                  Mandatory                
      Date                       Commitment         Amount Available
      ----                        Reduction          After Reduction
                                 ----------         ----------------
--------------------------------------------------------------------
March 31, 2000                     $875,000              $17,625,000
--------------------------------------------------------------------
June 30, 2000                      $875,000              $16,750,000
--------------------------------------------------------------------
September 30, 2000                 $875,000              $15,875,000
--------------------------------------------------------------------
December 31, 2000                  $875,000              $15,000,000
--------------------------------------------------------------------
March 31, 2001                   $1,125,000              $13,875,000
--------------------------------------------------------------------
June 30, 2001                    $1,125,000              $12,750,000
--------------------------------------------------------------------
September 30, 2001               $1,125,000              $11,625,000
--------------------------------------------------------------------
December 31, 2001                $1,125,000              $10,500,000
--------------------------------------------------------------------
March 31, 2002                   $1,000,000               $9,500,000
--------------------------------------------------------------------
June 30, 2002                    $1,000,000               $8,500,000
--------------------------------------------------------------------
September 30, 2002               $1,000,000               $7,500,000
--------------------------------------------------------------------
December 31, 2002                $1,000,000               $6,500,000
--------------------------------------------------------------------
March 31, 2003                   $1,000,000               $5,500,000
--------------------------------------------------------------------
June 30, 2003                    $1,000,000               $4,500,000
--------------------------------------------------------------------
September 30, 2003               $1,000,000               $3,500,000
--------------------------------------------------------------------
December 31, 2003                $1,000,000               $2,500,000
--------------------------------------------------------------------
March 31, 2004                   $1,250,000               $1,250,000
--------------------------------------------------------------------
June 30, 2004                    $1,250,000                       $0
--------------------------------------------------------------------
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                                      -4-


          In addition, if the Borrower raises additional capital through an
          equity sale, the Bank shall have the option to require the Borrower to
          apply up to 50% of the net sale proceeds from such sale to the
          reduction of the Commitment.  The proceeds will be applied on the date
          of the sale to the scheduled Commitment reductions in inverse order."

     (d)  Subsection (c) of Section 5.8 (Reporting Requirements) is deleted and
          ------------------------------------------------------               
     replaced with the following:

          "(c)   Monthly Accounts Receivable Aging Report and Financial
                 ------------------------------------------------------
          Statements.  As soon as available, and in any event within thirty (30)
          ----------                                                            
          days following the end of each month, copies of the following,
          certified by a Senior Officer of the Borrower:

          (i)    a report in form satisfactory to the Bank of the age of
          accounts receivable generated by the Borrower and each of its
          Subsidiaries; and

          (ii)   the consolidated and consolidating balance sheet and statements
          of operations of the Borrower and its Subsidiaries as at the end of
          and for such month and, with respect to the statements of operations,
          the portion of the fiscal year ended with such month, together with a
          report in form satisfactory to the Bank showing a comparison of such
          results with the Borrower's budget."

     (e)  Subsection (d) of Section 5.8 (Reporting Requirements) is deleted and
          ------------------------------------------------------               
     replaced with the following:

          "(d)   Actual and Projected Quarterly Capital Expenditures.  As soon 
                 ---------------------------------------------------     
          as available, and in any event within forty-five (45) days after the
          end of each quarterly fiscal period of the Borrower, a report in form
          satisfactory to the Bank indicating (i) the actual Capital
          Expenditures of the Borrower and its Subsidiaries for such fiscal
          quarter and (ii) the projected Capital Expenditures for the remainder
          of the fiscal year. The report shall also detail for both clauses (i)
          and (ii) above that portion of Capital Expenditures which comprises
          software development expenditures and shows both actual Capital
          Expenditures and software development expenditures compared with the
          budgeted amounts for such items."
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                                      -5-



     (f)  Section 5.8 (Reporting Requirements) is further amended by adding the
          ------------------------------------                                 
     following subsection (m):

          "(m)   Report of Customer Financings.  Within five (5) days after the
                 -----------------------------                                 
          occurrence of such event, a written notice detailing the substantive
          terms of each agreement the Borrower or any Subsidiary has entered
          into with a customer in which the Borrower or such Subsidiary has
          agreed to finance more than $150,000 of the implementation costs of
          product sold by the Borrower or such Subsidiary to such customer."

     (g)  Section 6.9 (Capital Expenditures) is deleted and replaced with the
          ----------------------------------                                 
     following:

          "Section 6.9. Capital Expenditures.  Make or permit to be made any
                        --------------------                                
          Capital Expenditure in any fiscal year, or commit to make any Capital
          Expenditure in any fiscal year, which when added to the aggregate
          Capital Expenditures of the Borrower and its Subsidiaries theretofore
          made or committed to be make in that fiscal year, would exceed the
          corresponding amount for such year as set forth below:


          -----------------------------------------------------------
                    Year               Permitted Capital Expenditures
                    ----               ------------------------------
          -----------------------------------------------------------
                    1999                        $3,550,000
          -----------------------------------------------------------
                    2000                        $4,100,000
          -----------------------------------------------------------
                    2001                        $4,720,000
          -----------------------------------------------------------
                    2002                        $5,750,000
          -----------------------------------------------------------
                    2003                        $5,950,000
          -----------------------------------------------------------
                    2004                        $5,950,000"
          -----------------------------------------------------------
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                                      -6-


     (h)  Section 6.10 (Minimum Consolidated GAAP Net Worth is deleted and
          -------------------------------------------------               
     replaced with the following:

          "Section 6.10 Minimum Consolidated GAAP Net Worth.  As of the end of
                        -----------------------------------                   
          any fiscal quarter, permit Consolidated GAAP Net Worth of the Borrower
          and its Subsidiaries to be less than an amount equal to (a) for the
          period to and including December 31, 1999, $26,000,000, plus 75% of
                                                                  ----       
          cumulative positive net income for each fiscal quarter following the
          fiscal quarter ending December 31, 1998, plus the amount of paid-in-
                                                   ----                      
          capital resulting from any issuance by the Borrower of its capital
          stock after the Closing Date to and including December 31, 1999 and
          (b) for all fiscal quarters after December 31, 1999, commencing with
          the fiscal quarter ended March 31, 2000, $33,900,000, plus 75% of
                                                                ----       
          cumulative positive net income for each fiscal quarter following the
          fiscal quarter ending December 31, 1999, plus the amount of paid-in-
                                                   ----                      
          capital resulting from any issuance by the Borrower of its capital
          stock after March 31, 2000."

     (i)  The number $17,000,000 appearing in Schedule 1.1 to the Credit
                                              ------------              
     Agreement is deleted and replaced with the number "$18,500,000."

     (j)  Exhibit A to the Credit Agreement is deleted and replaced with Exhibit
          ---------                                                      -------
     A to this Third Amendment.
     -                         

     Section 2. Conditions of Effectiveness.  This Third Amendment shall become
                ---------------------------                                    
effective when, and only if, the Bank shall have received on or before April 27,
1999 a counterpart of this Third Amendment executed by the Borrower and an
amendment fee of $250,000 and the following other conditions shall have been
satisfied on or before said date:

     (a)  the Bank shall have received a duly completed and executed revolving
     note of the Borrower in the amount of the Commitment in the form of Exhibit
                                                                         -------
     A hereto;
     -        

     (b)  the Bank shall have received a duly completed and executed Warrant, in
     the form of Exhibit B hereto, pursuant to which the Borrower grants to the
                 ---------                                                     
     Bank warrants to purchase 187,000 shares of Common Stock of the Borrower;

     (c)  the Bank shall have received a duly completed and executed
     registration rights agreement, in the form of Exhibit B hereto, relating to
                                                   ---------
     the Warrant to be issued pursuant to clause (b) above;

     (d)  the Bank shall have received a certificate of a Senior Officer of the
     Borrower stating that:
<PAGE>
 
                                      -7-


          (i)    the representations and warranties contained in Article 4 of
          the Credit Agreement and in the other Loan Documents are correct on
          and as of the date of such certificate as though made on and as of
          such date (or, if such representation or warranty is expressly stated
          to have been made as of a specific date, as of such specific date);

          (ii)   no Event of Default or Default has occurred and is continuing
          or would result from the signing of the amendment to the Credit
          Agreement or the transactions contemplated thereby; and

          (iii)  there has been no material adverse change in the financial
          conditions, operations, Properties, business or business prospects of
          the Borrower and its Subsidiaries, since December 31, 1998, the date
          of the last audited financial statements furnished to the Bank;

     (e)  the Bank shall have received a reaffirmation from the Borrower and its
     Subsidiaries, in a form acceptable to the Bank, that the Security Documents
     are in full force and effect and apply to the Credit Agreement as amended
     by this Third Amendment;

     (f)  the Bank shall have received the executed legal opinion of Rich, May,
     Bilodeau & Flaherty, P.C., counsel to the Borrower, in a form acceptable to
     the Bank and its counsel;

     (g)  the Bank shall have received copies of any amendments to the articles
     of incorporation and by-laws of the Borrower and each Subsidiary, which
     have been authorized or became effective since August 31, 1998, certified
     as complete and correct copies thereof by the Secretary or an Assistant
     Secretary of the Borrower or such Subsidiary, as applicable;

     (h)  the Bank shall have received a copy of the resolutions, in form and
     substance satisfactory to the Bank, of the Board of Directors of the
     Borrower, authorizing the execution, delivery and performance by the
     Borrower of this Third Amendment and the Warrant and Registration Rights
     Agreement relating thereto, certified by the Secretary or an Assistant
     Secretary of the Borrower, which certificate shall state that the
     resolutions thereby certified have not been amended, modified, revoked or
     rescinded;

     (i)  all corporate and legal proceedings and all instruments and agreements
     in connection with the transactions contemplated by this Third Amendment
     shall be satisfactory in form and substance to the Bank and the Bank shall
     have received any and all other information and documents with respect to
     the Borrower which it may reasonably request; and

     (j)  Day, Berry & Howard LLP, special counsel to the Bank, shall have
     received payment of its legal fees and disbursements relating to this Third
     Amendment.
<PAGE>
 
                                      -8-


     Section 3. Representations and Warranties of the Borrower.  The Borrower
                ----------------------------------------------               
represents as follows:

     (a)  The execution, delivery and performance by the Borrower of this Third
     Amendment has been duly authorized by all necessary corporate action and
     does not and will not (a) require any consent or approval of its
     shareholders; (b) violate any provisions of its certificate of
     incorporation or by-laws; (c) violate any provision of or require any
     filing, registration, consent or approval under, any law, rule, regulation
     (including without limitation, Regulation U and X), order, writ, judgment,
     injunction, decree, determination or award presently in effect having
     applicability to and binding upon the Borrower or any Subsidiary; (d)
     result in a breach of or constitute a default or require any consent under
     any indenture, mortgage or loan or credit agreement or any other material
     agreement, lease or instrument to which the Borrower or any Subsidiary is a
     party or by which it or its Properties may be bound; or (e) result in, or
     require, the creation or imposition of any Lien upon or with respect to any
     of the Properties now owned or hereafter acquired by the Borrower.

     (b)  The representations and warranties contained in Article 4 of the
     Credit Agreement, as amended by this Third Amendment, are correct in all
     material respects on and as of the date hereof as though made on and as of
     the date hereof, provided, however, that (a) each of Cost Review Services,
                      -----------------
     Inc. and TCM Services, Inc. have sold all of their assets to unrelated
     third parties and are currently inactive; (b) those certain Financing
     Statements filed in favor of the Bank and listing Cost Review Services,
     Inc. as debtor and TCM Services, Inc. as debtor have been terminated; and
     (c) the chief executive office and principal place of business of each of
     Cost Review Services, Inc. and TCM Services, Inc. are currently located at
     18881 Von Karman Avenue, Suite 1750, Irvine, California 92612.

     (c)  No Event of Default or Default has occurred and is continuing or would
     result from the signing of this Third Amendment or the transactions
     contemplated hereby.

     (d)  There has been no material adverse change in the financial condition,
     operations, Properties, business or business prospects of the Borrower and
     its Subsidiaries, if any, since the date of the last financial statements
     furnished to the Bank.

     (e)  No actions, suits or proceedings or investigations are pending or, as
     far as the Borrower can reasonably foresee, threatened against or affecting
     the Borrower or any Subsidiary, or any Property of any of them before any
     court, governmental agency or arbitrator, which if determined adversely to
     the Borrower or any Subsidiary would in any one case or in the aggregate
     have a Materially Adverse Effect.

     (f)  No information, exhibit or report furnished in writing by or on behalf
     of the Borrower or any officer or director of the Borrower to the Bank in
     connection with the negotiation of, or pursuant to the terms of this Third
     Amendment, contained when made 
<PAGE>
 
                                      -9-


     any material misstatement of fact or omitted to state a material fact
     necessary to make the statements contained therein not misleading.

     Section 4.  Reference to and Effect on the Credit Agreement.
                 ----------------------------------------------- 

     (a)  Upon the effectiveness of this Third Amendment, on and after the date
     hereof, each reference in the Credit Agreement to "this Credit Agreement",
     "hereunder", "hereof", "herein" or words of the like import shall mean and
     be a reference to the Credit Agreement as amended hereby.

     (b)  Except as specifically amended above, the Credit Agreement shall
     remain in full force and effect and is hereby ratified and confirmed.

     (c)  The execution, delivery and effectiveness of this Third Amendment
     shall not, except as expressly provided herein, operate as a waiver of any
     right, power or remedy of the Bank under the Credit Agreement, nor
     constitute a waiver of any provision of the Credit Agreement.

     Section 5.  Costs, Expenses and Taxes.  The Borrower agrees to pay on
                 -------------------------                                
demand all costs and expenses of the Bank in connection with the preparation,
execution and delivery of this Third Amendment including, without limitation,
the reasonable fees and out-of-pocket expenses of counsel for the Bank with
respect thereto.

     Section 6.  Execution in Counterparts.  This Third Amendment may be
                 -------------------------                              
executed in any number of counterparts, each of which when so executed and
delivered shall be deemed to be an original and all of which taken together
shall constitute but one and the same instrument.

     Section 7.  Governing Law.  This Third Amendment shall be governed by, and
                 -------------                                                 
construed in accordance with, the laws of the Commonwealth of Massachusetts.

     Section 8.  Defined Terms.  Capitalized terms used herein which are not
                 -------------                                              
expressly defined herein shall have the meanings ascribed to them in the Credit
Agreement.

     Section 9.  Interest Rate Protection.  Pursuant to Section 5.14 of the
                 ------------------------                                  
Credit Agreement, the Borrower shall enter into interest rate protection
arrangements acceptable to the Bank within 30 days after the date of this Third
Amendment to reflect the increased Commitment.

     Section 10. Evidence of Good Standing.  Within 60 days after the date of
                 -------------------------                                   
this Third Amendment, the Borrower shall provide the Bank with written evidence
of (a) the good standing of the Borrower in the Commonwealth of Massachusetts
and the State of Missouri; (b) the good standing of Core Securities Corp. in the
Commonwealth of Massachusetts; (c) the good standing of Protocol Work Systems,
Inc. in the Commonwealth of Massachusetts; and (d) the good standing of Core
Management, Inc. (Delaware) in the Commonwealth of Massachusetts and the State
of Delaware.
<PAGE>
 
                                      -10-


                 [Remainder of Page Intentionally Left Blank]
<PAGE>
 
                                      -11-


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


                                           CORE, INC.                       
                                                                            
                                                                            
                                           By  /s/ William E. Nixon         
                                              --------------------------    
                                              Name:   William E. Nixon      
                                              Title:  EVP & CFO             
                                                                            
                                                                            
                                                                            
                                           FLEET NATIONAL BANK              
                                                                            
                                                                            
                                           By  /s/ Jeffrey A. Simpson       
                                              --------------------------    
                                              Name:   Jeffrey A. Simpson    
                                              Title:  Vice President