<PAGE>

                                                                    EXHIBIT 10.4

                                FIRST AMENDMENT
                                      TO
                        NEWPORT NEWS SHIPBUILDING INC.
          CHANGE IN CONTROL SEVERANCE BENEFIT PLAN FOR KEY EXECUTIVES



     The Newport News Shipbuilding Inc. Change in Control Severance Benefit Plan
for Key Executives (As Amended and Restated Effective March 23, 1999) (the
"Plan") is hereby amended, effective immediately prior to the Consummation of
the Offer (as defined in the Agreement and Plan of Merger among General Dynamics
Corporation, Grail Acquisition Corporation and Newport News Shipbuilding Inc.,
dated as of April 24, 2001), as follows:


     1.   Paragraph A of Section 1 (the definition of "Change in Control") is
          amended by adding a new clause (6) thereof to read as follows:

          "(6)  the Consummation of the Offer (as defined in the Agreement and
                Plan of Merger among General Dynamics Corporation, Grail
                Acquisition Corporation and the Company, dated as of April 24,
                2001) (the "Merger Agreement")."

     2.   Paragraph B of Section 1 (the definition of "Constructive
          Termination") is amended by adding the following at the end thereof:

          "Notwithstanding anything to the contrary in this Plan, no
          Constructive Termination under clause (1) above shall be deemed to
          have occurred prior to the Effective Time (as defined in the Merger
          Agreement) so long as General Dynamics Corporation or the Company has
          not taken or caused to be taken any affirmative action to diminish the
          Key Executive's status, position, duties or responsibilities from
          those in effect immediately prior to the Change in Control. From and
          after the Effective Time, the immediately preceding sentence shall
          cease to apply and shall not in any manner limit the right of a Key
          Executive to claim, upon
<PAGE>

          or following the Effective Time, that a Constructive Termination has
          occurred under the terms of clause (1) above."

     3.   The heading and introduction to Section 4 is amended by inserting the
          term "(I)" immediately following the phrase "Eligibility for
                                                       ---------------
          Benefits." and immediately before the term "(i)".
          --------

     4.   Subparagraph A of Section 4(I) is amended by adding the following at
          the end thereof:

          "; provided, that any amount actually payable to the Key Executive
             --------
          pursuant to clause (1) of Section F of Article V of the Newport News
          Shipbuilding Inc. Annual Incentive Plan for the year in which the
          Change in Control occurs shall be taken into account for purposes of
          subclause (i) of subparagraph (b) above as the Key Executive's annual
          award under the Newport News Shipbuilding Inc. Annual Incentive Plan
          for that year of the Key Executive's employment with NNS Companies;
          provided, further, that any amount actually payable to the Key
          --------  -------
          Executive pursuant to clause (2) of Section F of Article V of the
          Newport News Shipbuilding Inc. Annual Incentive Plan for the year in
          which the Change in Control occurs shall not be taken into account for
          purposes of subclause (i) of subparagraph (b) above, and in such event
          the awards for the last three years of the Key Executive's employment
          will be deemed to be the awards for the three years immediately
          preceding the year in which the Change in Control occurs."

     5.   Subparagraph B of Section 4(I) is amended by adding the following at
          the end thereof:

          "; provided, that any amount actually payable to the Key Executive
             --------
          pursuant to clause (2) of Section F of Article V of the Newport News
          Shipbuilding Inc. Annual Incentive Plan for the year in which the
          Change in Control occurs shall not be taken into account for purposes
          of subclause (i) of subparagraph (b) above as the Key Executive's
          annual award under the Newport News Shipbuilding Inc. Annual Incentive
          Plan for that
<PAGE>

                                                                               3

          year of the Key Executive's employment with NNS Companies, and in such
          event the awards for the last three years of the Key Executive's
          employment will be deemed to be the awards for the three years
          immediately preceding the year in which the Change in Control occurs.

     6.   Section 4(I)(i)(F) is deleted, and Section 4(I)(i)(G) is relettered as
          Section 4(I)(i)(F).

     7.   Section 4(II) is added to read as follows:

          "(II)  During the first 30 days immediately following the first
          anniversary of the Change in Control, any member of Executive Group I
          may voluntarily elect to separate from service as an employee with the
          NNS Companies, whether or not such individual shall have suffered a
          Constructive Termination prior to such voluntary separation from
          service, in which case the individual shall be provided with the
          severance and other benefits described in subparagraphs A, C, D and E
          of Section 4(I) above."

     8.   Paragraph D of Section 14 is hereby amended in its entirety to read as
          follows:

          "Notwithstanding Section 9, all or part of the benefits payable under
          the Plan may be paid from the trust established under the Trust
          Agreement for Newport News Shipbuilding Inc. Benefits Protection Plans
          (the "Rabbi Trust"). To the extent a Key Executive receives benefits
          from the Rabbi Trust, the Company's obligation under the Plan will be
          satisfied. Upon a Change in Control, the Company shall be required to
          fund the Rabbi Trust in accordance with the provisions of Section 1(g)
          of the Rabbi Trust."


     Full Force and Effect.  Except as expressly amended hereby, the Plan shall
     ---------------------
continue in full force and effect in accordance with the terms thereof on the
date hereof.

     Governing Law.  This Amendment shall be governed by and construed in
     -------------
accordance with the laws of the Commonwealth of
<PAGE>

                                                                               4

Virginia applicable to agreements made and entirely to be performed within such
jurisdiction.



     IN WITNESS WHEREOF, this Amendment is hereby executed this _____ day of
________, 2001.


                                   NEWPORT NEWS SHIPBUILDING INC.



                                   By:_______________________
                                      Vice President, Human
                                      Resources and EH&S


ATTEST:



By:_________________________
Title: