<PAGE>
 
                                                                     EXHIBIT 4.1

NEITHER THIS WARRANT NOR THE SHARES ISSUABLE UPON THE EXERCISE OF THIS WARRANT
HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND
APPLICABLE STATE SECURITIES LAWS AND MAY NOT BE SOLD, TRANSFERRED OR OTHERWISE
DISPOSED OF UNLESS THEY HAVE BEEN REGISTERED UNDER THE ACT AND APPLICABLE STATE
SECURITIES LAWS OR UNLESS AN EXEMPTION FROM REGISTRATION IS AVAILABLE.


                                  CORE, INC.
                           Warrant for Common Stock


No. R-2                                                           April 27, 1999



                           Void After June 30, 2004
                           ------------------------

     THIS CERTIFIES that, for value received, FLEET NATIONAL BANK, or its
registered assigns, is entitled to subscribe for and purchase from CORE, INC., a
Massachusetts corporation (hereinafter called the "Corporation"), at the price
of $12.00 per share (such price, as it may be from time to time adjusted as
hereinafter provided, being hereinafter called the "Warrant Exercise Price"), at
any time after the date hereof and on or prior to June 30, 2004, up to 187,000
(subject to adjustment as hereinafter provided) fully paid and nonassessable
shares of Common Stock, $.10 par value (hereinafter called the "Common Stock"),
of the Corporation, subject, however, to the provisions and upon the terms and
conditions hereinafter set forth.  This Warrant is issued pursuant to the Credit
Agreement, dated as of August 31, 1998, as amended by the First Amendment to the
Credit Agreement dated as of December 31, 1998, the Second Amendment to the
Credit Agreement dated as of February 19, 1999 and the Third Amendment to the
Credit Agreement dated as of April 27, 1999 (as so amended, the "Credit
Agreement"), between the Corporation and Fleet National Bank.  This Warrant,
each such other warrant and any warrant or warrants subsequently issued upon
exchange or transfer hereof or thereof are hereinafter collectively called the
"Warrants".

     Section 1.  Exercise of Warrant.
                 ------------------- 

          (a)    Method of Exercise; Net Issue Exercise.  The rights 
                 --------------------------------------
     represented by this Warrant may be exercised by the holder hereof, in whole
     at any time or from time to time in part, but not as to a fractional share
     of Common Stock, by the surrender of this Warrant, together with a properly
     completed notice of exercise in the form of Annex A hereto (a "Notice of
     Exercise"), at the office of the Corporation specified in or pursuant to
     Section 9 hereof. Upon receipt by the 
<PAGE>
 
     Corporation of a Notice of Exercise, the Warrant Expense Price shall be
     deemed paid and, subject to paragraph (d) of this Section 1, the
     Corporation shall issue to the holder hereof a number of shares of Common
     Stock equal to (A) the number of shares of Common Stock acquirable upon
     exercise in full of this Warrant (or, if applicable, the portion hereof
     being exercised), as at such date, multiplied by (B) the balance remaining
     after deducting (x) the Warrant Exercise Price, as in effect on such date,
     from (y) the fair market value of one share of Common Stock as at such date
     and dividing the result by (C) such fair market value.

          (b)    Definition of Fair Market Value.  For purposes of paragraph (a)
                 -------------------------------                                
     above, the fair market value of the Common Stock shall be determined as
     follows:  if the Common Stock is listed or admitted to trading on one or
     more national securities exchanges, the average of the last reported sales
     prices per share regular way or, in case no such reported sales takes place
     on any such day, the average of the last reported bid and asked prices per
     share regular way, in either case on the principal national securities
     exchange on which the Common Stock is listed or admitted to trading, for
     the thirty (30) trading days immediately preceding the date upon which the
     fair market value is determined (the "Determination Date"); if the Common
     Stock is not listed or admitted to trading on a national securities
     exchange but is quoted by the NASD Automated Quotation System ("NASDAQ"),
     the average of the last reported sales prices per share regular way or, in
     case no reported sale takes place on any such day or the last reported
     sales prices are not then quoted by NASDAQ, the average for each such day
     of the last reported bid and asked prices per share, for the thirty (30)
     trading days immediately preceding the Determination Date as furnished by
     the National Quotation Bureau Incorporated or any similar successor
     organization; and if the Common Stock is not listed or admitted to trading
     on a national securities exchange or quoted by NASDAQ or any other
     nationally recognized quotation service, the fair market value shall be the
     fair value thereof determined in good faith by the Board of Directors of
     the Corporation; provided, however, that if the holders of Warrants
                      --------- -------                                 
     outstanding representing a majority of the shares of Common Stock
     acquirable upon exercise of the Warrants object, within a reasonable time
     after being given notice thereof, to such determination, the fair market
     value shall be determined in good faith by an independent investment
     banking firm selected jointly by the Board of Directors of the Corporation
     and the holders of Warrants outstanding representing a majority of the
     shares of Common Stock acquirable upon exercise of the Warrants or, if that
     selection cannot be made within fifteen (15) days, by an independent
     investment banking firm selected by the American Arbitration Association in
     accordance with its rules.  Anything in this paragraph (b) to the contrary
     notwithstanding, the fair market value of this Warrant or any portion
     thereof as of any Determination Date shall be equal to (i) the fair market
     value of the shares of Common Stock issuable upon exercise of this Warrant
     (or 

                                      -2-
<PAGE>
 
     such portion thereof) (determined in accordance with the foregoing
     provisions of this paragraph (b)) minus (ii) the aggregate Warrant Exercise
     Price of the Warrant (or such portion thereof).

          (c)    Delivery of Certificates, Etc.  In the event of any exercise of
                 -----------------------------                                  
     the rights represented by this Warrant, a certificate or certificates. for
     the shares of Common Stock so purchased, registered in the name of the
     holder, shall be delivered to the holder hereof within a reasonable time,
     not exceeding ten (10) days, after the rights represented by this Warrant
     shall have been so exercised; and, unless this Warrant has expired, a new
     Warrant representing the number of shares (except a remaining fractional
     share), if any, with respect to which this Warrant shall not then have been
     exercised shall also be issued to the holder hereof within such time.  The
     person in whose name any certificate for shares of Common Stock is issued
     upon exercise of this Warrant shall for all purposes be treated as having
     become the holder of record of such shares on the date on which the Warrant
     was surrendered, together with a properly completed Notice of Exercise, and
     payment of the Warrant Exercise Price and any applicable taxes was made,
     except that, if the date of such surrender and payment is a date on which
     the stock transfer books of the Corporation are closed, such person shall
     be treated as having become the holder of such shares at the close of
     business on the next succeeding date on which the stock transfer books are
     open.

          (d)    Cash Out Option.  In lieu of issuing shares of Common Stock 
                 ---------------
     upon receipt of a Notice of Exercise pursuant to paragraph (a) above, the
     Corporation shall have the option, exercisable within ten (10) days after
     receipt of such Notice of Exercise, to repurchase the Warrant (or portion
     thereof which is to be exercised) in consideration of the payment to the
     holder of the Warrant in U.S. Dollars of an amount equal to the fair market
     value of the Warrant (or such portion thereof), such payment to be made to
     the holder on the date the Corporation exercises such option.

     Section 2.  Adjustment of Number of Shares.  Upon each adjustment of the
                 ------------------------------                              
Warrant Exercise Price as provided in Section 3, the holder of this Warrant
shall thereafter be entitled to purchase, at the Warrant Exercise Price
resulting from such adjustment and subject to the provisions of Section 1, the
number of shares (calculated to the nearest tenth of a share) obtained by
multiplying the Warrant Exercise Price in effect immediately prior to such
adjustment by the number of shares purchasable pursuant hereto immediately prior
to such adjustment and dividing the product thereof by the Warrant Exercise
Price resulting from such adjustment.

     Section 3.  Adjustment of Price Upon Issuance of Common Stock.  The
                 -------------------------------------------------      
adjustments provided for in this Section 3 shall be made for any events
occurring on or after April 27, 1999.

                                      -3-
<PAGE>
 
          (a)    Subdivision or Combination of Stock.  In case the Corporation
                 -----------------------------------                          
     shall at any time subdivide its outstanding shares of Common Stock into a
     greater number of shares, the Warrant Exercise Price in effect immediately
     prior to such subdivision shall be proportionately reduced, and conversely,
     in case the outstanding shares of Common Stock of the Corporation shall be
     combined into a smaller number of shares, the Warrant Exercise Price in
     effect immediately prior to such combination shall be proportionately
     increased.

          (b)    Stock Dividends.  In case the Corporation shall declare a 
                 ---------------     
     dividend or make any other distribution upon any stock of the Corporation
     payable in Common Stock, or rights to subscribe for or to purchase, or
     options for the purchase of, Common Stock or any stock or securities
     convertible or exchangeable for Common Stock (such rights or options being
     herein called "Options" and such convertible or exchangeable stock or
     securities being herein called "Convertible Securities"), any Common Stock,
     Options or Convertible Securities, as the case may be, issuable in payment
     of such dividend or distribution shall be treated as having been issued or
     sold without consideration, and the Warrant Exercise Price shall be reduced
     as if the Corporation had subdivided its outstanding shares of Common Stock
     into a greater number of shares, as provided in paragraph (a) above.

          (c)    Reorganization, Reclassification, Consolidation, Merger or 
                 ----------------------------------------------------------
     Sale.  If any capital reorganization or reclassification of the capital
     ----
     stock of the Corporation or any consolidation or merger of the Corporation
     with or into another corporation, or the sale of all or substantially all
     of its assets to another corporation shall be effected in such a way
     (including, without limitation, by way of consolidation or merger) that
     holders of Common Stock shall be entitled to receive stock, securities or
     assets with respect to or in exchange for Common Stock, then, as a
     condition of such reorganization, reclassification, consolidation, merger
     or sale, lawful and adequate provisions shall be made whereby each holder
     of Warrants shall thereafter have the right to receive, upon the basis and
     upon the terms and conditions specified herein and in lieu of the shares of
     Common Stock of the Corporation immediately theretofore receivable upon the
     exercise of such Warrants, such shares of stock, securities or assets as
     may be issued or payable with respect to or in exchange for a number of
     outstanding shares of such Common Stock equal to the number of shares of
     such stock immediately theretofore so receivable had such reorganization,
     reclassification, consolidation, merger or sale not taken place, and in any
     such case appropriate provision shall be made with respect to the rights
     and interests of such holder to the end that the provisions hereof
     (including, without limitation, provisions for adjustment of the Warrant
     Exercise Price) shall thereafter be applicable, as nearly practicable, in
     relation to any shares of stock, securities or assets thereafter
     deliverable upon the exercise of such exercise rights (including, 

                                      -4-
<PAGE>
 
     if necessary to effect the adjustments contemplated herein, an immediate
     adjustment, by reason of such reorganization, reclassification,
     consolidation, merger or sale, of the Warrant Exercise Price to the value
     for the Common Stock reflected by the terms of such reorganization,
     reclassification, consolidation, merger or sale if the value so reflected
     is less than the Warrant Exercise Price in effect immediately prior to such
     reorganization, reclassification, consolidation, merger or sale). The
     Corporation will not effect any such consolidation or merger, or any sale
     of all or substantially all of its assets and properties, unless prior to
     the consummation thereof the successor corporation (if other than the
     Corporation) resulting from such consolidation or merger or the corporation
     purchasing such assets shall assume by written instrument, executed and
     mailed or delivered to each holder of Warrants at the last address of such
     holder appearing on the records of the Corporation, the obligation to
     deliver to such holder such shares of stock, securities or assets as, in
     accordance with the foregoing provisions, such holder may be entitled to
     receive.

          (d)    Notice of Adjustment.  Upon any adjustment of the Warrant 
                 --------------------                              
     Exercise Price, then and in each such case the Corporation shall give
     written notice thereof, by first class mail postage prepaid, addressed to
     each holder of Warrants at the address of such holder as shown on the
     records of the Corporation, which notice shall state the Warrant Exercise
     Price resulting from such adjustment, setting forth in reasonable detail
     the method of calculation and the facts upon which such calculation is
     based.

          (e)    Certain Events.  If any event occurs as to which in the 
                 --------------                          
     opinion of the Board of Directors of the Corporation the other provisions
     of this Section 3 are not strictly applicable or if strictly applicable
     would not fairly protect the exercise rights of this Warrant, in accordance
     with the essential intent and principles of such provisions to protect
     against dilution, then such Board of Directors shall in good faith make an
     adjustment in the application of such provisions, in accordance with such
     essential intent and principles, so as to protect such exercise rights as
     aforesaid.

          (f)    Stock to Be Reserved.  The Corporation will at all times 
                 --------------------         
     reserve and keep available out of its authorized Common Stock or its
     treasury shares, solely for the purpose of issue upon the exercise of this
     Warrant as herein provided, such number of shares of Common Stock as shall
     then be issuable upon the exercise of this Warrant. The Corporation
     covenants that all shares of Common Stock which shall be so issued shall be
     duly and validly issued and fully paid and nonassessable and free from all
     taxes, liens and charges with respect to the issue thereof, and, without
     limiting the generality of the foregoing, the Corporation covenants that it
     will from time to time take all such action as may be requisite to assure
     that the par value per share of the Common Stock is at all times equal to
     or less than the effective Warrant Exercise Price. The Corporation will
     take all

                                      -5-
<PAGE>
 
     such action as may be necessary to assure that all such shares of Common 
     Stock may be so issued without violation of any applicable law or 
     regulation, or of any requirements of any national securities exchange upon
     which the Common Stock of the Corporation may be listed; provided, however,
                                                              --------- ------- 
     that this sentence shall not obligate the Corporation to register such
     shares under the Securities Act of 1933, as amended (the "Securities Act"),
     or any applicable state securities laws or to take any action to enable the
     sale or transfer of such shares to be made in accordance with Rule 144
     under the Securities Act.  The Corporation will not take any action which
     results in any adjustment of the Warrant Exercise Price if the total number
     of shares of Common Stock issued and issuable after such action upon
     exercise of this Warrant would exceed the total number of shares of Common
     Stock then authorized by the Corporation's Articles of Organization. The
     Corporation has not granted and will not grant any right of first refusal
     with respect to shares issuable upon exercise of this Warrant, and there
     are no preemptive rights associated with such shares.

          (g)    Issue Tax.  The issuance of certificates for shares of Common
                 ---------                                                    
     Stock upon exercise of this Warrant shall be made without charge to the
     holder hereof for any issuance tax in respect thereof, provided that the
     Corporation shall not be required to pay any tax which may be payable in
     respect of any transfer involved in the issuance and delivery of any
     certificate in a name other than that of such holder.

          (h)    Maintenance of Register.  The Corporation shall keep at its 
                 -----------------------       
     office specified in or pursuant to Section 9 hereof a register in which the
     Corporation shall provide for the registration of this Warrant and for the
     registration of transfer and exchange of this Warrant. The holder of this
     Warrant may, at its option, and either in person or by its duly authorized
     attorney, surrender the same for registration of transfer or exchange at
     such office of the Corporation and, without charge to such holder (except
     for taxes imposed in connection with any transfer of this Warrant or, if
     applicable, any portion hereof in a name other than that of such holder),
     receive in exchange therefor a Warrant or Warrants each exercisable for
     such number of shares of Common Stock as such holder may request (and
     collectively exercisable for the same aggregate number of shares of Common
     Stock with respect to which this Warrant or, if applicable, such portion
     hereof surrendered for transfer or exchange shall not then have been
     exercised) and registered in the name of such person or persons as may be
     designated by such holder. This Warrant, when presented or surrendered for
     registration of transfer or exchange, shall be accompanied by a written
     instrument of transfer, satisfactory in form to the Corporation, duly
     executed by the holder of hereof. Every Warrant so made and delivered in
     exchange for this Warrant shall in all other respects be in the same form
     and have the same terms as this Warrant. No transfer or exchange of this
     Warrant shall be valid (x) unless made in the foregoing manner at such
     office or agency and (y) unless registered under the Securities Act and any
     applicable state securities laws or

                                      -6-
<PAGE>
 
     unless an exemption from such registration is available. The Corporation
     will at no time close its transfer books against the transfer of this
     Warrant or the transfer of the shares of Common Stock issued or issuable
     upon the exercise of this Warrant in any manner which interferes with the
     timely exercise of this Warrant.

          (i)    Definition of Common Stock.  As used herein the term "Common
                 --------------------------                                  
     Stock" shall mean and include the Common Stock, $.10 par value, of the
     Corporation as authorized on April 27, 1999 and also any capital stock of
     any class of the Corporation thereafter authorized which shall not be
     limited to a fixed sum or percentage in respect of the rights of the
     holders thereof to participate in dividends or in the distribution of
     assets upon the voluntary or involuntary liquidation, dissolution or
     winding up of the Corporation, but in no event shall include the Preferred
     Stock; provided, however, that the shares purchasable pursuant to this
            --------- -------                                              
     Warrant shall include only shares designated as Common Stock, $.10 par
     value, of the Corporation on April 27, 1999, or shares of any class or
     classes resulting from any reclassification or reclassifications thereof
     which are not limited to any such fixed sum or percentage and are not
     subject to redemption by the Corporation and, in case at any time there
     shall be more than one such resulting class, the shares of each class then
     so issuable shall be substantially in the proportion which the total number
     of shares of such class resulting from all such reclassifications bears to
     the total number of shares of all such classes resulting from all such
     reclassifications.

     Section 4.  Notices of Record Dates.  In the event of
                 -----------------------                  

          (1)    any taking by the Corporation of a record of the holders of any
     class of securities for the purpose of determining the holders thereof who
     are entitled to receive any dividend or other distribution (other than cash
     dividends out of earned surplus), or any right to subscribe for, purchase
     or otherwise acquire any shares of stock of any class or any other
     securities or property, or to receive any other right, or

          (2)    any capital reorganization of the Corporation, any
     reclassification or recapitalization of the capital stock of the
     Corporation or any sale of all or substantially all the assets of the
     Corporation to or consolidation or merger of the Corporation with or into
     any other corporation, or

          (3)    any voluntary or involuntary dissolution, liquidation or
     winding-up of the Corporation,

then and in each such event the Corporation will give notice to the holder of
this Warrant specifying (i) the date on which any such record is to be taken for
the purpose of such dividend, distribution or right and stating the amount and
character of such dividend, distribution or right, and (ii) the date on which
any such reorganization, 

                                      -7-
<PAGE>
 
reclassification, recapitalization, sale, consolidation, merger, dissolution,
liquidation or winding up is to take place, and the time, if any is to be fixed,
as of which the holders of record of Common Stock will be entitled to exchange
their shares of Common Stock for securities or other property deliverable upon
such reorganization, reclassification, recapitalization, sale, consolidation,
merger, dissolution, liquidation or winding-up. Such notice shall be given at
least twenty (20) days and not more than ninety (90) days prior to the date
therein specified, and such notice shall state that the action in question or
the record date is subject to the effectiveness of a registration statement
under the Securities Act of 1933, as amended (the "Securities Act") or to a
favorable vote of stockholders, if either is required.

     Section 5.  Registration Rights.  The rights of the holder hereof with
                 -------------------                                       
respect to the registration under the Securities Act of the shares of Common
Stock issuable upon the exercise of this Warrant are set forth in the
Registration Rights Agreement, dated as of April 27, 1999, between the
Corporation and Fleet National Bank, as the same may hereafter be amended,
supplemented, restricted or otherwise modified from time to time.

     Section 6.  No Stockholder Rights or Liabilities.  This Warrant shall not
                 ------------------------------------                         
entitle the holder hereof to any voting rights or other rights as a stockholder
of the Corporation.  No provision hereof, in the absence of affirmative action
by the holder hereof to purchase shares of Common Stock, and no mere enumeration
herein of the rights or privileges of the holder hereof, shall give rise to any
liability of such holder for the Warrant Exercise Price or as a stockholder of
the Corporation, whether such liability is asserted by the Corporation or by
creditors of the Corporation.

     Section 7.  Investment Representation and Legend.  The holder, by
                 ------------------------------------                 
acceptance of the Warrant, represents and warrants to the Corporation that it is
acquiring the Warrant and the shares of Common Stock (or other securities)
issuable upon the exercise hereof for investment purposes only and not with a
view towards the resale or other distribution thereof and agrees that the
Corporation may affix upon this Warrant the following legend:

          "NEITHER THIS WARRANT NOR THE SHARES ISSUABLE UPON THE EXERCISE OF
     THIS WARRANT HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
     AMENDED, AND APPLICABLE STATE SECURITIES LAWS AND MAY NOT BE SOLD,
     TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS THEY HAVE BEEN REGISTERED UNDER
     THE ACT AND APPLICABLE STATE SECURITIES LAWS OR UNLESS AN EXEMPTION FROM
     REGISTRATION IS AVAILABLE."

The holder, by acceptance of this Warrant, further agrees that the Corporation
may affix the following legend to certificates for shares of Common Stock issued
upon exercise of this Warrant:

                                      -8-
<PAGE>
 
          "THE SHARES EVIDENCED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
     UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND APPLICABLE STATE
     SECURITIES LAWS AND MAY NOT BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF
     UNLESS THEY HAVE BEEN REGISTERED UNDER THE ACT AND APPLICABLE STATE
     SECURITIES LAWS OR UNLESS AN EXEMPTION FROM REGISTRATION IS AVAILABLE."

     Section 8.  Lost, Stolen, Mutilated or Destroyed Warrant.  If this Warrant
                 --------------------------------------------                  
is lost, stolen, mutilated or destroyed, the Corporation may, upon delivery of
an indemnity agreement reasonably satisfactory to the Corporation (which in the
case of Fleet National Bank shall be Fleet National Bank's own unsecured
agreement of indemnity) and such other terms as the Corporation may otherwise in
its discretion reasonably impose (which shall, in the case of a mutilated
Warrant, include the surrender thereof), issue a new Warrant of like
denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed.
Any such new Warrant shall constitute an original contractual obligation of the
Corporation, whether or not the allegedly lost, stolen, mutilated or destroyed
Warrant shall be at any time enforceable by anyone.

     Section 9.  Notices.  All notices, requests, and other communications
                 -------                                                  
required or permitted to be given or delivered hereunder shall be in writing,
and shall be delivered, or shall be sent by certified or registered mail,
postage prepaid and addressed, (i) if to the holder, to such holder at the
address shown on such holder's Warrant or Warrant Shares or at such other
address as shall have been furnished to the Corporation by notice from such
holder and (ii) if to the Corporation, to it at 18881 Von Karman Avenue, Suite
1750, Irvine, CA 92612, Attention: Chief Financial Officer or at such other
address as shall have been specified to the holder by notice from the
Corporation.

                 [Remainder of Page Intentionally Left Blank]

                                      -9-
<PAGE>
 
     IN WITNESS WHEREOF, CORE, INC. has executed this Warrant on and as of the
day and year first above written.


                                          CORE, INC.


                                          By: /s/ William E. Nixon
                                              -----------------------
                                              Name:  William E. Nixon
                                              Title: EVP & CFO

                                      -10-