<PAGE>

                                                                   EXHIBIT 10.42

                   AMENDMENT NO. 1 TO STOCKHOLDERS AGREEMENT
                   -----------------------------------------

          AMENDMENT NO, 1 TO STOCKHOLDERS AGREEMENT, dated as of December 15,
1998 (the "Amendment"), by and among Select Medical Corporation, a Delaware
corporation (the "Company"), the stockholders of the Company whose names appear
in Schedule I annexed hereto (collectively, the "Original Stockholders"), and
the additional stockholders of the Company whose names appear in Schedule II
annexed hereto (collectively, the "Additional Stockholders"), amending the
Stockholders Agreement dated as of February 5, 1997 (the "Agreement") by and
among the Company, the Original Stockholders and the other stockholders of the
Company named as parties thereto at the foot thereof.

          WHEREAS, the Company, the Original Stockholders, the Additional
Stockholders and certain other stockholders of the Company (collectively, the
"December 1998 Investors") are parties to a Securities Purchase Agreement dated
as of December 15, 1998, providing, among other things, for the sale to such
December 1998 Investors of an aggregate 21,224,489 shares (the "December 1998
Shares") of the Company's Common Stock, par value $.01 (the "Common Stock"); and

          WHEREAS, the Company, the Original Stockholders and the other
stockholders of the Company named as parties to the Agreement entered into the
Agreement in order, among other things, to specify certain rights and
obligations of each of the parties thereto with respect to the shares of Common
Stock held by each of them; and

          WHEREAS, the Agreement may be amended by the written consent of the
Company and the Original Stockholders; and

          WHEREAS, the Company and the Original Stockholders now desire to amend
the Agreement in the manner set forth below in order, among other things, to
include the December 1998 Shares as "Stockholder Shares" under the Agreement and
to include the Additional Stockholders as "Investors" and "Stockholders" under
the Agreement;

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

     Section 1.     Definitions; References.  Unless otherwise specifically
                    -----------------------
defined herein, each term used herein which is defined in the Agreement shall
have the meaning assigned to such term in the Agreement. Each reference to
"hereof," "hereunder," "herein," and "hereby" and each other similar reference
and each reference to "this Agreement" and each other similar reference
contained in the Agreement shall from after the date hereof refer to the
Agreement as amended by this Amendment .

     Section 2.     Additional Stockholders as Investors and Stockholders.
                    -----------------------------------------------------
Effective as of the date hereof, each of the Additional Stockholders shall
become an Investor, and thereby a Stockholder, under the Agreement, and by such
Additional Stockholder's execution of this
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Amendment, each of such Additional Stockholders agrees to comply with and be
bound by all of the provisions of the Agreement as an Investor and Stockholder
thereunder, as if an original signatory thereto. For purposes of the Agreement,
the December 1998 Shares shall be deemed to be included in the term "Common
Stock" and "Stockholder Shares".

     Section 3.     Amendment to Second Unnumbered Paragraph.  The first
                    ----------------------------------------
sentence of the second unnumbered paragraph of the Agreement is hereby amended
to read in its entirety as follows:

                    "Certain of the Investors will purchase shares of the
          Company's Common Stock, par value $.01 per share (the "February 1997
          Common"), and the Company's Class A Preferred Stock (the "Class A
          Preferred"), pursuant to a Purchase Agreement, dated as of February 5,
          1997 (the "1997 Purchase Agreement"), among the Company and such
          Investors. Certain of the Investors and the Additional Stockholders
          (as such term is defined in Amendment No. 1 to Stockholders Agreement
          dated as of December 15, 1998 among the Company and the parties
          thereto (the "Amendment")) will also purchase shares of the Company's
          Common Stock, par value $.01 per share (collectively with the February
          1997 Common, the "Common Stock") pursuant to a Securities Purchase
          Agreement, dated as of December 15, 1998 (the "1998 Purchase
          Agreement" and, collectively with the 1997 Purchase Agreement, the
          "Purchase Agreements" or the "Purchase Agreement"), among the Company,
          such Investors and the Additional Stockholders."

     Section 4.     Amendment to Fourth Unnumbered Paragraph.  The fourth
                    ----------------------------------------
unnumbered paragraph of the Agreement is hereby amended to read in its entirety
as follows:

                    "The execution and delivery of this Agreement is a condition
          to certain of the Investors' purchase of Common Stock and Class A
          Preferred pursuant to the 1997 Purchase Agreement. The execution and
          delivery of the Amendment is a condition to the purchase by certain of
          the Investors and the Additional Stockholders of Common Stock pursuant
          to the 1998 Purchase Agreement."

     Section 5.     Addition to Schedule of Stockholders.  The Schedule of
                    ------------------------------------
Stockholders annexed to the Agreement is hereby amended by adding the names and
addresses of each of the Additional Stockholders set forth in Schedule II
hereto.

     Section 6.     Effect of Amendment.  Except as expressly provided in this
                    -------------------
Amendment, nothing herein shall affect or be deemed to affect any provisions of
the Agreement, and except only to the extent that they may be varied hereby, all
of the terms of the Agreement shall remain unchanged and in full force and
effect.

     Section 7.     Applicable Law.  This Amendment shall be construed and
                    --------------
enforced in accordance with, and the rights of the parties shall be governed by,
the laws of the State of Delaware without reference to the principles of
conflicts of law.

                                       2
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     Section 8.     Counterparts.  This Amendment may be executed in
                    ------------
counterparts, all of which together shall constitute one agreement binding on
all the parties hereto, notwithstanding that all such parties are not
signatories to the original or the same counterpart. Each party shall become
bound by this Amendment immediately upon affixing such party's signature hereto.

     IN WITNESS WHEREOF, the Company, the Original Stockholders and the
Additional Stockholders have executed this Amendment as of the day and year
first above written.

                              SELECT MEDICAL CORPORATION

                              By  /s/ Rocco A. Ortenzio
                                -------------------------------------
                              Name:
                              Title:

                              ORIGINAL STOCKHOLDERS:

                              GOLDER, THOMA, CRESSEY, RAUNER FUND V, L.P.
                              By GTCR V, L.P., General Partner
                              By Golder, Thoma, Cressey, Rauner, Inc., General
                              partner

                              By  /s/ Donald Edwards
                                -------------------------------------
                              Name:
                              Title:

                              WELSH, CARSON, ANDERSON & STOWE VII, L.P.
                              By WCAS VII Partners, L.P., General Partner

                              By  /s/ Laura VanBuren
                                -------------------------------------
                              Name:
                              Title:

                                       3
<PAGE>

                              Bruce K. Anderson
                              Russell L. Carson
                              Anthony J. de Nicola
                              Thomas E. Mclnerney
                              James B. Hoover
                              Robert A. Minicucci
                              Andrew M. Paul
                              Paul B. Queally
                              Richard H. Stowe
                              Laura M. VanBuren
                              Patrick J. Welsh

                              By  /s/ Laura VanBuren
                                -----------------------------
                                  Laura M. VanBuren
                                  Individually and as
                                  Attorney-in-fact

                               /s/  Rocco A. Ortenzio
                              -------------------------------
                                  Rocco Ortenzio

                               /s/  Robert A. Ortenzio
                              -------------------------------
                                  Robert Ortenzio


                              ADDITIONAL STOCKHOLDERS:

                              WCAS CAPITAL PARTNERS III, L.P.
                              By WCAS CP III Associates, L.L.C., General Partner

                              By /s/ Laura VanBuren
                                -----------------------------------
                              Name:
                              Title:

                                 /s/ Lawrence B. Sorrel
                              -------------------------------------
                                  Lawrence B. Sorrel

                                       4
<PAGE>

                                 /s/ Priscilla A. Newman
                              --------------------------------
                                  Priscilla A. Newman


                                 /s/ Rudolph Rupert
                              --------------------------------
                                  Rudolph Rupert


                                 /s/ D. Scott Mackesy
                              --------------------------------
                                  D. Scott Mackesy

                              GTCR FUND VI, L.P.
                              By GTCR Partners VI, L.P., General Partner
                              By GTCR Golder Rauner, L.L.C., General Partner

                              By /s/ Donald Edwards
                                ----------------------------------------------
                              Name:
                              Its:  Principal

                              THOMA CRESSEY FUND VI, L.P.
                              By TC Partners VI, L.P., General Partner
                              By Thoma Cressey Equity Partners Inc., General
                              Partner

                              By /s/ [Illegible]
                                ----------------------------------------------
                              Name:
                              Title:

                              SELECT HEALTHCARE INVESTORS I, L.P.

                              By /s/ Rocco A. Ortenzio
                                ----------------------------------------------
                              Name:
                              Title:

                                       5
<PAGE>

                              ANVERS, L.P.

                              By:  FSIP, LLC
                                  General Partner

                              By /s/ Leopold Swergold
                                ----------------------------------------------
                              Name:  Leopold Swergold
                              Title:    Senior Managing Director

                              ANVERS, L.P.

                              By:  FSIP, LLC
                                  General Partner

                              By /s/ Leopold Swergold
                                ----------------------------------------------
                              Name:  Leopold Swergold
                              Title:    Senior Managing Director

                              GTCR VI EXECUTIVE FUND, L.P.
                              By GTCR Partners VI, L.P., General Partner
                              By GTCR Golder Rauner L.L.C. General Partner

                              By /s/ Donald Edwards
                                ----------------------------------------------
                              Name:
                              Its:  Principal

                              GTCR ASSOCIATES VI
                              By GTCR Partners VI, L.P., Managing General
                              Partner
                              By GTCR Golder Rauner, L.L.C., General Partner

                              By /s/ Donald Edwards
                                ----------------------------------------------
                              Name:
                              Its:  Principal

                                  /s/ Bryan C. Cressey
                                ----------------------------------------------
                              Bryan C. Cressey

                                       6