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                                UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549

                             -------------------
                               AMENDMENT NO. 1
                                      to

                                  FORM 10-K

                   AMENDMENT TO APPLICATION ON REPORT FILED
                   PURSUANT TO SECTION 12, 13 OR 15 (d) OF
                     THE SECURITIES EXCHANGE ACT OF 1934

                     FOR THE YEAR ENDED DECEMBER 31, 1998

                         GENERAL DYNAMICS CORPORATION

                           3190 Fairview Park Drive
                      Falls Church, Virginia 22042-4253

                        Commission File Number 1-3671

       The undersigned registrant hereby amends the following items, financial
statements, exhibits or other portions of its 1998 Annual Report on Form 10-K as
set forth in the pages attached hereto:

               Index to Exhibits

               Exhibit 99F Annual Report on Form 11-K
               for the General Dynamics Corporation Savings
               and Stock Investment Plan

               Exhibit 99G Annual Report on Form 11-K
               for the General Dynamics Corporation Hourly
               Employees Savings and Stock Investment Plan

       Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this amendment to be signed on its behalf by the
undersigned thereunto duly authorized.

                                             GENERAL DYNAMICS CORPORATION
                                                     (Registrant)

                                             By    /s/  David A. Savner
                                                -------------------------
                                                     David A. Savner
                                                        Secretary

Dated:    June 30, 1999


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<PAGE>   2

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
 Note           Exhibit
Number          Number                                    Description
------          -------                                   -----------

<S>             <C>            <C>
   (5)           3-1A          --Restated Certificate of Incorporation, effective May 21, 1991
  (12)           3-2D          --Bylaws as amended effective October 1, 1997
  (11)           4             --Letter re agreement to furnish copy of indenture
   (1)          10-1A          --Amendment of Mining Leases between American National Bank and Trust
                                 of Chicago, Trustee, and La Salle National Bank, Trustee, to Freeman Coal Mining
                                 Corporation, dated January 1, 1960
   (1)          10-1B          --Amendatory Agreement between Freeman United Coal Mining Company and
                                 American National Bank and Trust Company, as Trustee, and La Salle National Bank,
                                 as Trustee, dated January 1, 1975
   (3)          10-6A          --General Dynamics Corporation Incentive Compensation Plan adopted February 3, 1988,
                                 approved by the shareholders on May 4, 1988
   (4)          10-6B          --General Dynamics Corporation Incentive Compensation Plan (as amended),
                                 approved by shareholders on May 1, 1991
   (4)          10-7E          --Facilities Contract DAAE07-90-E-A001 dated June 24, 1990, between General Dynamics
                                 Land Systems, Inc. and the United States relating to government-owned facilities and
                                 equipment at the Lima Army Tank Plant, Lima, Ohio
 * (7)          10-8B          --General Dynamics Corporation Retirement Plan for Directors adopted March 6, 1986, as
                                 amended May 5, 1993
  (11)          10-14A         --Lease Agreement dated December 20, 1996, between Electric Boat Corporation and the
                                 Rhode Island Economic Development Corporation
 * (6)          10-18          --Employment Agreement between the company and James R. Mellor dated as of
                                 March 17, 1993
 * (9)          10-18A         --Amendment to employment agreement between the company and James R. Mellor dated as of
                                 October 3, 1995
* (11)          10-18B         --Amendment to employment agreement between the company and James R. Mellor dated  as of
                                 November 5, 1996
   (9)          10-25          --Lease Agreement dated January 14, 1982, between Bath Iron Works Corporation and the City
                                 of Portland, Maine, relating to pier facilities in the Portland, Maine harbor
   (9)          10-26          --Lease Agreement dated January 14, 1982, between Bath Iron Works Corporation and the State
                                 of Maine, relating to a dry dock facility in the Portland, Maine harbor
  (10)          10-28          --Asset Purchase and Sale Agreement, dated November 6, 1996, as amended December 20, 1996,
                                 between the company and Lockheed Martin Corporation
* (11)          10-29          --Employment agreement between the company and Nicholas D. Chabraja dated
                                 November 12, 1996
* (11)          10-30          --General Dynamics Corporation Incentive Compensation Plan adopted February 5, 1997,
                                 approved by shareholders on May 7, 1997
* (12)          10-31          --Retirement Benefit Agreement between the company and Gordon R. England dated
                                 February 14, 1997
  (12)          10-32          --Credit Enhancement Agreement between Bath Iron Works Corporation and the City of
                                 Bath, Maine dated September 19, 1997, relatingto the development program of facilities
                                 in Bath, Maine
* (12)          10-33          --Retirement Benefit Agreement between the company and Michael J. Mancuso dated
                                 March 6, 1998
* (12)          10-34          --Consulting agreement between the company and Paul G. Kaminski dated August 18, 1997
  (13)          10-36          --Stock Purchase Agreement dated as of October 8, 1998, between the company and NASSCO
                                 Holdings Incorporated and the stockholders of NASSCO Holdings Incorporated
* (14)          10-37          --Retirement Benefit Agreement between the company and David A. Savner dated March 4, 1998
</TABLE>


<PAGE>   3


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
 Note           Exhibit
Number          Number                                           Description
------          -------                                          -----------

<S>             <C>            <C>
(14)            10-38          --Lease Agreement dated January 1, 1991, between National Steel and Shipbuilding Company and
                                 the San Diego Unified Port District, relating to facilities in the San Diego, California harbor
(14)            10-38A         --Amendment of Lease Agreement between National Steel and Shipbuilding Company and the
                                 San Diego Unified Port District, dated December 6, 1994
(14)            10-39          --Capital Construction Fund Agreement, dated September 13, 1988, between National Steel and
                                 Shipbuilding Company and the United States of America, represented by the Maritime
                                 Administrator, Department of Transportation
(14)            10-39A         --Capital Construction Fund Agreement-Addendum No. 1, dated September 13, 1988, between
                                 National Steel and Shipbuilding Company and the United States of America, represented by
                                 the Maritime Administrator, Department of Transportation
(14)            10-39B         --Capital Construction Fund Agreement-Addendum No. 2, dated October 29, 1992, between
                                 National Steel and Shipbuilding Company and the United States of America, represented by
                                 the Maritime Administrator, Department of Transportation
(14)            10-39C         --Capital Construction Fund Agreement-Addendum No. 3, dated August 27, 1993, between
                                 National Steel and Shipbuilding Company and the United States of America, represented by
                                 the Maritime Administrator, Department of Transportation
(14)            10-39D         --Capital Construction Fund Agreement-Addendum No. 4, dated August 28, 1997, between
                                 National Steel and Shipbuilding Company and the United States of America, represented by
                                 the Maritime Administrator, Department of Transportation
(14)            10-39E         --Capital Construction Fund Agreement-Addendum No. 5, dated October 29, 1997, between
                                 National Steel and Shipbuilding Company and the United States of America, represented by
                                 the Maritime Administrator, Department of Transportation
(16)            10-40          --Agreement and Plan of Merger dated May 16, 1999 between General Dynamics Corporation,
                                 Tara Acquisition Corporation and Gulfstream Aerospace Corporation
(16)            10-41          --Voting Agreement dated  May 16, 1999 between General Dynamics Corporation and certain
                                 stockholders of Gulfstream Aerospace Corporation
(17)            10-42          --Stock Purchase Agreement (without Schedules and Exhibits) dated as of June 21, 1999 between
                                 General Dynamics, Contel Federal Systems, Inc. and GTE Corporation
(14)            13             --1998 Annual Report (pages 20 through 44)
(14)            21             --Subsidiaries
(14)            23             --Consent of Independent Public Accountants
(14)            24             --Power of Attorney of the Board of Directors
(14)            27             --Financial Data Schedule
(14)            27-A           --Amended Financial Data Schedule for the year ended December 31, 1997
(14)            27-B           --Amended Financial Data Schedule for the nine months ended September 28, 1997
(14)            27-C           --Amended Financial Data Schedule for the six months ended June 29, 1997
(14)            27-D           --Amended Financial Data Schedule for the three months ended March 30, 1997
(15)            99D            --1997 Annual Reprt on Form 11-K for the General Dynamics Corporation Savings and Stock
                                 Investment Plan
(15)            99E            --1997 Annual Reprt on Form 11-K for the General Dynamics Corporation Hourly Employees
                                 Savings and Stock Investment Plan
                99F            --1998 Annual Report on Form 11-K for the General Dynamics Corporation Savings and Stock
                                 Investment Plan
                99G            --1998 Annual Report on Form 11-K for the General Dynamics Corporation Hourly Employees
                                 Savings and Stock Investment Plan
</TABLE>

*      Indicates a management contract or compensatory plan or arrangement
       required to be filed pursuant to Item 14(c) of Form 10-K.

                                      NOTES

 (1)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1980, and filed with the Commission March
         31, 1981, and incorporated herein by reference (Commission File No.
         1-3671).

 (2)     Not used.

 (3)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1987, and filed with the Commission March
         17, 1988, and incorporated herein by reference (Commission File No.
         1-3671).

 (4)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1990, and filed with the Commission March
         29, 1991, and incorporated herein by reference (Commission File No.
         1-3671).

<PAGE>   4

 (5)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1991, and filed with the Commission March
         26, 1992, and incorporated herein by reference (Commission File No.
         1-3671).


(6)      Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1992, and filed with the Commission March
         30, 1993, and incorporated herein by reference (Commission File No.
         1-3671).

 (7)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1994, and filed with the Commission March
         9, 1995, and incorporated herein by reference (Commission File No.
         1-3671).

 (8)     Not used.

 (9)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1995, and filed with the Commission March
         21, 1996, and incorporated herein by reference (Commission File No.
         1-3671).

(10)     Filed as an exhibit to the company's current report on Form 8-K filed
         with the Commission January 15, 1997, and incorporated herein by
         reference (Commission File No. 1-3671).

(11)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1996, and filed with the Commission March
         21, 1997, and incorporated herein by reference (Commission File No.
         1-3671).

(12)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1997, and filed with the Commission March
         18, 1998, and incorporated herein by reference (Commission File No.
         1-3671).

(13)     Filed as an exhibit to the company's current report on Form 8-K filed
         with the Commission November 25, 1998, and incorporated herein by
         reference (Commission File No. 1-3671).

(14)     Filed as an exhibit to the company's annual report on Form 10-K for
         the year ending December 31, 1998, and filed with the Commission March
         18, 1999, and incorporated herein by reference (Commission File No.
         1-3671).

(15)     Filed as an exhibit to the company's annual report on Form 10-K/A for
         the year ending December 31, 1997, and filed with the Commission June
         26, 1998, and incorporated herein by reference (Commission File No.
         1-3671).

(16)     Filed as an exhibit to the company's quarterly report on Form 10-Q for
         the quarterly period ended April 4, 1999, and filed with the
         Commission May 18, 1999, and incorporated herein by reference
         (Commission File No. 1-3671).

(17)     Filed as an exhibit to the company's current report on Form 8-K filed
         with the Commission June 24, 1999, and incorporated herein by reference
         (Commission File No. 1-3671).
