<PAGE>   1
    AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON DECEMBER 31, 1997



                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                               ------------------

                                    FORM S-8

                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933

                               ------------------

                           COMPAQ COMPUTER CORPORATION
             (Exact Name of Registrant as Specified in Its Charter)

           Delaware                                      76-0011617
 (State or Other Jurisdiction of                        (IRS Employer
 Incorporation or Organization)                       Identification No.)

            20555 S.H. 249
            Houston, Texas                                  77070
 (Address of Principal Executive Offices)                 (Zip Code)


                               ------------------

              Tandem Computers Incorporated 401(k) Investment Plan
                            (Full Title of the Plan)

                               ------------------

                                J. David Cabello
               Senior Vice President, General Counsel & Secretary
                           Compaq Computer Corporation
                                 20555 S.H. 249
                              Houston, Texas 77070
                     (Name and Address of Agent for Service)

                               ------------------

                                 (281) 370-0670
          (Telephone Number, Including Area Code, of Agent for Service)


                         CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
============================================================================================================
      Title of                                    Proposed              Proposed
     Securities              Amount               Maximum               Maximum
        To be                 to be            Offering Price          Aggregate             Amount of
   Registered (1)          Registered            Per Share           Offering Price      Registration Fee
---------------------- -------------------- --------------------- --------------------- --------------------
<S>                    <C>                  <C>                   <C>                   <C>
   Common Stock of     
   Compaq Computer       370,000 shares           $53.6875            $19,864,375             $5.860
     Corporation
============================================================================================================
</TABLE>


(1) Estimated solely for the purpose of calculating the registration fee
pursuant to Rule 457 based upon the average of the high and low prices of the
Common Stock reported in the New York Stock Exchange consolidated reporting
system on December 26, 1997.



<PAGE>   2


                                     Part II

               Information Required in the Registration Statement


Item 3. Incorporation of Documents by Reference

         The following documents have been previously filed with the SEC and are
incorporated by reference into this Registration Statement:

         1. Compaq's Annual Report on Form 10-K for the year ended 
            December 31, 1996;

         2. Compaq's Quarterly Reports on Form 10-Q for the quarters ended
            March 31, 1997, June 30, 1997 and September 30, 1997;

         3. Compaq's Current Reports on Form 8-K as filed on October 16, 1997
            and November 21, 1997;

         4. The description of the Compaq's common stock contained in
            Compaq's Registration Statement on Form 8-A; and

         5. The Plan's annual report on Form 11-K as filed on December 31, 1997.

         Compaq is also incorporating by reference additional documents that we
may file with the SEC between the date of the Prospectus to which this
Registration Statement relates and the date of the filing of a post-effective
amendment which indicates that all securities offered have been sold or which
deregisters all securities then remaining unsold.

         Copies of the documents incorporated by reference above may be obtained
from Compaq without charge, except the exhibits (unless we have specifically
incorporated by reference an exhibit in this Prospectus), by writing to:

                  Compaq Computer Corporation
                  20555 SH 249
                  Houston, Texas 77070
                  Telephone: (800) 433-2391
                  Attention:  Investor Relations


Item 5.  Interests of Named Experts and Counsel.

     The legality of the common stock offered by this Prospectus has been passed
upon for Compaq by Linda S. Auwers, Vice President and Associate General Counsel
of Compaq. Ms. Auwers has options to purchase Compaq common stock and owns
shares of Compaq common stock as a participant in an employee benefit plan.

<PAGE>   3

Item 6.  Indemnification of Directors and Officers.

         Exculpation. Section 102(b)(7) of the Delaware General Corporation Law
(the "DGCL") permits a corporation to include in its certificate of
incorporation a provision eliminating or limiting the personal liability of a
director to the corporation or its stockholders for monetary damages for breach
of fiduciary duty as a director, provided that such provision may not eliminate
or limit the liability of a director for any breach of the director's duty of
loyalty to the corporation or its stockholders, for acts or omissions not in
good faith or which involve intentional misconduct or a knowing violation of
law, for the payment of unlawful dividends, or for any transaction from which
the director derived an improper personal benefit.

         Compaq's Restated Certificate of Incorporation limits the personal
liability of a director to Compaq and its stockholders for monetary damages for
a breach of fiduciary duty as a director to the fullest extent permitted by the
DGCL.

         Indemnification. Delaware law permits a corporation to indemnify its 
officers and directors under any circumstances.

         Compaq's Bylaws provide for indemnification of directors and officers
of Compaq against liability to the fullest extent permitted by applicable law.

         Insurance. Compaq has in effect directors' and officers' liability 
insurance and fiduciary liability insurance.

Item. 8  Exhibits

Exhibit No.
-----------

 4.1    Tandem Computers Incorporated 401(k) Investment Plan.

 5.1    Opinion of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, as to the legality
        of the securities being registered.

23.1    Consent of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, is included in the
        opinion filed as Exhibit 5.1 to this Registration Statement.

23.2    Consent of Ernst & Young LLP, Independent
        Auditors.

23.3    Consent of Price Waterhouse LLP, Independent Accountants.

24.1    Powers of Attorney are included on the signature page of this
        Registration Statement.

<PAGE>   4

Item 9.  Undertakings.

         Compaq hereby undertakes:

         (1) To file, during any period in which offers or sales are being made,
a post-effective amendment to this Registration Statement to include any
material information with respect to the plan of distribution not previously
disclosed in the Registration Statement or any material change to such
information in the Registration Statement;

         (2) That, for the purpose of determining any liability under the
Securities Act of 1933, each such post-effective amendment shall be deemed to be
a new Registration Statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof; and

         (3) To remove from registration by means of a post-effective amendment
any of the securities being registered which remain unsold at the termination of
the offering.

         The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of
Registrant's annual report pursuant to Section 13(a) or Section 15(d) of the
Securities Exchange Act of 1934 that is incorporated by reference in the
Registration Statement shall be deemed to be a new Registration Statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.

         Insofar as indemnification for liabilities arising under the Securities
Act of 1933 may be permitted to directors, officers and controlling persons of
Registrant pursuant to the provisions described in Item 15 above, or otherwise,
Registrant has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by Registrant of expenses
incurred or paid by a director, officer or controlling person of Registrant in
the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, Registrant will, unless in the opinion of its counsel the matter has
been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Act and will be governed by the final adjudication of
such issue.



<PAGE>   5


                        SIGNATURES AND POWER OF ATTORNEY

         Pursuant to the requirements of the Securities Act of 1933, the
Registrant certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, and the State of Texas, on this 31st day of
December, 1997.

                                   COMPAQ COMPUTER CORPORATION


                                    By:      /s/ J. David Cabello
                                       ----------------------------------------
                                       J. David Cabello, Senior Vice President
                                       and General Counsel


<PAGE>   6


                        SIGNATURES AND POWER OF ATTORNEY

         We, the undersigned officers and directors of Compaq Computer
Corporation, do hereby constitute and appoint Eckhard Pfeiffer, Earl L. Mason
and J. David Cabello, or any one of them, our true and lawful attorneys and
agents, to do any and all acts and things in our name and on our behalf in our
capacities as directors and officers, and to execute any and all instruments for
us and in our names in the capacities indicated below, which said attorneys and
agents, or either one of them, may deem necessary or advisable to enable said
corporation to comply with the Securities Act of 1933, as amended, and any
rules, regulations, and requirements of the Securities and Exchange Commission,
in connection with the Company's registration statements on Form S-8 regarding
the Compaq Computer Corporation Deferred Compensation and Supplemental Savings
Plan, including specifically, but without limitation, power and authority to
sign for us or any of us, in our names in the capacities indicated below, such
registration statement on Form S-8 and any and all amendments thereto; and we do
each hereby ratify and confirm all that the said attorneys and agents, or either
of them, shall do or cause to be done by virtue hereof. The following persons
executed this power of attorney in the capacities and on the dates indicated
below.

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities indicated below.

<TABLE>
<CAPTION>
Signature                           Title                                             Date
---------                           -----                                             ----
<S>                                 <C>                                        <C>
/s/ Eckhard Pfeiffer                President, Chief Executive Officer          December 31, 1997
---------------------------         and Director (principal executive
(Eckhard Pfeiffer)                  officer)


/s/ Earl L. Mason                   Senior Vice President and                   December 31, 1997
---------------------------         Chief Financial Officer (principal
 (Earl L. Mason)                    financial and accounting officer)


/s/ Benjamin M. Rosen               Chairman of the Board of Directors          December 31, 1997
---------------------------
(Benjamin M. Rosen)


/s/ Lawrence T. Babbio              Director                                    December 31, 1997
---------------------------
(Lawrence T. Babbio)


/s/ Robert Ted Enloe, III           Director                                    December 31, 1997
---------------------------
(Robert Ted Enloe, III)


/s/ George H. Heilmeier             Director                                    December 31, 1997
---------------------------
(George H. Heilmeier)


/s/ George E.R. Kinnear II          Director                                    December 31, 1997
---------------------------
(George E.R. Kinnear II)


/s/ Peter N. Larson                 Director                                    December 31, 1997
---------------------------
(Peter N. Larson)
</TABLE>

<PAGE>   7
<TABLE>
<S>                                 <C>                                        <C>
                                    Director                                    December 31, 1997
---------------------------
(Kenneth L. Lay)


/s/ Thomas J. Perkins               Director                                    December 31, 1997
---------------------------
(Thomas J. Perkins)


                                    Director                                    December 31, 1997
---------------------------
(Kenneth Roman)


/s/ Lucille S. Salhany              Director                                    December 31, 1997
---------------------------
(Lucille S. Salhany)
</TABLE>




<PAGE>   8




                                  EXHIBIT INDEX

Exhibit
-------
 4.1    Tandem Computers Incorporated 401(k) Investment Plan.

 5.1    Opinion of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, as to the legality
        of the securities being registered.

23.1    Consent of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, is included in the
        opinion filed as Exhibit 5.1 to this Registration Statement.

23.2    Consent of Ernst & Young LLP, Independent
        Auditors.

23.3    Consent of Price Waterhouse LLP, Independent Accountants.

24.1    Powers of Attorney are included on the signature page of this
        Registration Statement.
[{"type": "S-8", "sequence": "1", "description": "COMPAQ COMPUTER CORPORATION", "secsgml_size_bytes": 15318}]
{"company-data": {"conformed-name": "COMPAQ COMPUTER CORP", "cik": "0000714154", "assigned-sic": "3571", "irs-number": "760011617", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-43595", "film-number": "97747663"}, "business-address": {"street1": "20555 S H 249", "city": "HOUSTON", "state": "TX", "zip": "77070", "phone": "7133700670"}, "mail-address": {"street1": "POST OFFICE BOX 692000 MS 110701", "street2": "POST OFFICE BOX 692000 MS 110701", "city": "HOUSTON", "state": "TX", "zip": "77269-2000"}}
1
    AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON DECEMBER 31, 1997

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                               ------------------

                                    FORM S-8

                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933

                               ------------------

                           COMPAQ COMPUTER CORPORATION
             (Exact Name of Registrant as Specified in Its Charter)

           Delaware                                      76-0011617
 (State or Other Jurisdiction of                        (IRS Employer
 Incorporation or Organization)                       Identification No.)

            20555 S.H. 249
            Houston, Texas                                  77070
 (Address of Principal Executive Offices)                 (Zip Code)

                               ------------------

              Tandem Computers Incorporated 401(k) Investment Plan
                            (Full Title of the Plan)

                               ------------------

                                J. David Cabello
               Senior Vice President, General Counsel & Secretary
                           Compaq Computer Corporation
                                 20555 S.H. 249
                              Houston, Texas 77070
                     (Name and Address of Agent for Service)

                               ------------------

                                 (281) 370-0670
          (Telephone Number, Including Area Code, of Agent for Service)

                         CALCULATION OF REGISTRATION FEE
============================================================================================================
      Title of                                    Proposed              Proposed
     Securities              Amount               Maximum               Maximum
        To be                 to be            Offering Price          Aggregate             Amount of
   Registered (1)          Registered            Per Share           Offering Price      Registration Fee
---------------------- -------------------- --------------------- --------------------- --------------------
Common Stock of     
   Compaq Computer       370,000 shares           $53.6875            $19,864,375             $5.860
     Corporation
============================================================================================================
(1) Estimated solely for the purpose of calculating the registration fee
pursuant to Rule 457 based upon the average of the high and low prices of the
Common Stock reported in the New York Stock Exchange consolidated reporting
system on December 26, 1997.
2

                                     Part II

               Information Required in the Registration Statement

Item 3. Incorporation of Documents by Reference

         The following documents have been previously filed with the SEC and are
incorporated by reference into this Registration Statement:

         1. Compaq's Annual Report on Form 10-K for the year ended 
            December 31, 1996;

         2. Compaq's Quarterly Reports on Form 10-Q for the quarters ended
            March 31, 1997, June 30, 1997 and September 30, 1997;

         3. Compaq's Current Reports on Form 8-K as filed on October 16, 1997
            and November 21, 1997;

         4. The description of the Compaq's common stock contained in
            Compaq's Registration Statement on Form 8-A; and

         5. The Plan's annual report on Form 11-K as filed on December 31, 1997.

         Compaq is also incorporating by reference additional documents that we
may file with the SEC between the date of the Prospectus to which this
Registration Statement relates and the date of the filing of a post-effective
amendment which indicates that all securities offered have been sold or which
deregisters all securities then remaining unsold.

         Copies of the documents incorporated by reference above may be obtained
from Compaq without charge, except the exhibits (unless we have specifically
incorporated by reference an exhibit in this Prospectus), by writing to:

                  Compaq Computer Corporation
                  20555 SH 249
                  Houston, Texas 77070
                  Telephone: (800) 433-2391
                  Attention:  Investor Relations

Item 5.  Interests of Named Experts and Counsel.

     The legality of the common stock offered by this Prospectus has been passed
upon for Compaq by Linda S. Auwers, Vice President and Associate General Counsel
of Compaq. Ms. Auwers has options to purchase Compaq common stock and owns
shares of Compaq common stock as a participant in an employee benefit plan.
3

Item 6.  Indemnification of Directors and Officers.

         Exculpation. Section 102(b)(7) of the Delaware General Corporation Law
(the "DGCL") permits a corporation to include in its certificate of
incorporation a provision eliminating or limiting the personal liability of a
director to the corporation or its stockholders for monetary damages for breach
of fiduciary duty as a director, provided that such provision may not eliminate
or limit the liability of a director for any breach of the director's duty of
loyalty to the corporation or its stockholders, for acts or omissions not in
good faith or which involve intentional misconduct or a knowing violation of
law, for the payment of unlawful dividends, or for any transaction from which
the director derived an improper personal benefit.

         Compaq's Restated Certificate of Incorporation limits the personal
liability of a director to Compaq and its stockholders for monetary damages for
a breach of fiduciary duty as a director to the fullest extent permitted by the
DGCL.

         Indemnification. Delaware law permits a corporation to indemnify its 
officers and directors under any circumstances.

         Compaq's Bylaws provide for indemnification of directors and officers
of Compaq against liability to the fullest extent permitted by applicable law.

         Insurance. Compaq has in effect directors' and officers' liability 
insurance and fiduciary liability insurance.

Item. 8  Exhibits

Exhibit No.
-----------

 4.1    Tandem Computers Incorporated 401(k) Investment Plan.

 5.1    Opinion of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, as to the legality
        of the securities being registered.

23.1    Consent of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, is included in the
        opinion filed as Exhibit 5.1 to this Registration Statement.

23.2    Consent of Ernst & Young LLP, Independent
        Auditors.

23.3    Consent of Price Waterhouse LLP, Independent Accountants.

24.1    Powers of Attorney are included on the signature page of this
        Registration Statement.
4

Item 9.  Undertakings.

         Compaq hereby undertakes:

         (1) To file, during any period in which offers or sales are being made,
a post-effective amendment to this Registration Statement to include any
material information with respect to the plan of distribution not previously
disclosed in the Registration Statement or any material change to such
information in the Registration Statement;

         (2) That, for the purpose of determining any liability under the
Securities Act of 1933, each such post-effective amendment shall be deemed to be
a new Registration Statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof; and

         (3) To remove from registration by means of a post-effective amendment
any of the securities being registered which remain unsold at the termination of
the offering.

         The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of
Registrant's annual report pursuant to Section 13(a) or Section 15(d) of the
Securities Exchange Act of 1934 that is incorporated by reference in the
Registration Statement shall be deemed to be a new Registration Statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.

         Insofar as indemnification for liabilities arising under the Securities
Act of 1933 may be permitted to directors, officers and controlling persons of
Registrant pursuant to the provisions described in Item 15 above, or otherwise,
Registrant has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by Registrant of expenses
incurred or paid by a director, officer or controlling person of Registrant in
the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, Registrant will, unless in the opinion of its counsel the matter has
been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Act and will be governed by the final adjudication of
such issue.
5

                        SIGNATURES AND POWER OF ATTORNEY

         Pursuant to the requirements of the Securities Act of 1933, the
Registrant certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, and the State of Texas, on this 31st day of
December, 1997.

                                   COMPAQ COMPUTER CORPORATION

                                    By:      /s/ J. David Cabello
                                       ----------------------------------------
                                       J. David Cabello, Senior Vice President
                                       and General Counsel
6

                        SIGNATURES AND POWER OF ATTORNEY

         We, the undersigned officers and directors of Compaq Computer
Corporation, do hereby constitute and appoint Eckhard Pfeiffer, Earl L. Mason
and J. David Cabello, or any one of them, our true and lawful attorneys and
agents, to do any and all acts and things in our name and on our behalf in our
capacities as directors and officers, and to execute any and all instruments for
us and in our names in the capacities indicated below, which said attorneys and
agents, or either one of them, may deem necessary or advisable to enable said
corporation to comply with the Securities Act of 1933, as amended, and any
rules, regulations, and requirements of the Securities and Exchange Commission,
in connection with the Company's registration statements on Form S-8 regarding
the Compaq Computer Corporation Deferred Compensation and Supplemental Savings
Plan, including specifically, but without limitation, power and authority to
sign for us or any of us, in our names in the capacities indicated below, such
registration statement on Form S-8 and any and all amendments thereto; and we do
each hereby ratify and confirm all that the said attorneys and agents, or either
of them, shall do or cause to be done by virtue hereof. The following persons
executed this power of attorney in the capacities and on the dates indicated
below.

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities indicated below.
Signature                           Title                                             Date
---------                           -----                                             ----
/s/ Eckhard Pfeiffer                President, Chief Executive Officer          December 31, 1997
---------------------------         and Director (principal executive
(Eckhard Pfeiffer)                  officer)

/s/ Earl L. Mason                   Senior Vice President and                   December 31, 1997
---------------------------         Chief Financial Officer (principal
 (Earl L. Mason)                    financial and accounting officer)

/s/ Benjamin M. Rosen               Chairman of the Board of Directors          December 31, 1997
---------------------------
(Benjamin M. Rosen)

/s/ Lawrence T. Babbio              Director                                    December 31, 1997
---------------------------
(Lawrence T. Babbio)

/s/ Robert Ted Enloe, III           Director                                    December 31, 1997
---------------------------
(Robert Ted Enloe, III)

/s/ George H. Heilmeier             Director                                    December 31, 1997
---------------------------
(George H. Heilmeier)

/s/ George E.R. Kinnear II          Director                                    December 31, 1997
---------------------------
(George E.R. Kinnear II)

/s/ Peter N. Larson                 Director                                    December 31, 1997
---------------------------
(Peter N. Larson)
7
Director                                    December 31, 1997
---------------------------
(Kenneth L. Lay)

/s/ Thomas J. Perkins               Director                                    December 31, 1997
---------------------------
(Thomas J. Perkins)

                                    Director                                    December 31, 1997
---------------------------
(Kenneth Roman)

/s/ Lucille S. Salhany              Director                                    December 31, 1997
---------------------------
(Lucille S. Salhany)
8

                                  EXHIBIT INDEX

Exhibit
-------
 4.1    Tandem Computers Incorporated 401(k) Investment Plan.

 5.1    Opinion of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, as to the legality
        of the securities being registered.

23.1    Consent of Linda S. Auwers, Vice President and
        Associate General Counsel of the Company, is included in the
        opinion filed as Exhibit 5.1 to this Registration Statement.

23.2    Consent of Ernst & Young LLP, Independent
        Auditors.

23.3    Consent of Price Waterhouse LLP, Independent Accountants.

24.1    Powers of Attorney are included on the signature page of this
        Registration Statement.