<PAGE>   1
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 19, 1998
                                                     REGISTRATION NO. 333-

================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM S-8

                             REGISTRATION STATEMENT
                                      UNDER
                     THE SECURITIES ACT OF 1933, AS AMENDED

                               VISX, INCORPORATED
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

<TABLE>
<S>                                                        <C>       
                  DELAWARE                                              06-1161793
(STATE OR OTHER JURISDICTION OF INCORPORATION              (I.R.S. EMPLOYER IDENTIFICATION NO.)
              OR ORGANIZATION)
</TABLE>


                             3400 CENTRAL EXPRESSWAY
                          SANTA CLARA, CALIFORNIA 95051
                    (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)

                                 1995 STOCK PLAN

                            (FULL TITLE OF THE PLAN)

                                  MARK B. LOGAN
          CHAIRMAN OF THE BOARD, PRESIDENT AND CHIEF EXECUTIVE OFFICER
                               VISX, INCORPORATED
                             3400 CENTRAL EXPRESSWAY
                          SANTA CLARA, CALIFORNIA 95051
            (NAME, ADDRESS AND TELEPHONE NUMBER OF AGENT FOR SERVICE)

                                   COPIES TO:
                             KATRINA J. CHURCH, ESQ.
                               VISX, INCORPORATED
                             3400 CENTRAL EXPRESSWAY
                          SANTA CLARA, CALIFORNIA 95051
                                 (408) 733-2020


<PAGE>   2
                         CALCULATION OF REGISTRATION FEE


<TABLE>
<CAPTION>
====================================================================================================================================
                                                                       PROPOSED MAXIMUM       PROPOSED MAXIMUM
TITLE OF SECURITIES TO BE REGISTERED(1)              AMOUNT TO BE       OFFERING PRICE       AGGREGATE OFFERING        AMOUNT OF
                                                      REGISTERED           PER SHARE              PRICE(2)          REGISTRATION FEE
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                  <C>               <C>                   <C>                    <C>      
1995 Stock Plan
  Common Stock, $0.01 par value..................         455,204           $43.19              $19,660,260.76          $5,799.78
------------------------------------------------------------------------------------------------------------------------------------
====================================================================================================================================
</TABLE>


(1)   In addition, pursuant to Rule 416(c) under the Securities Act of 1933, as
      amended (the "Securities Act"), this Registration Statement also covers an
      indeterminate amount of interests to be offered or sold pursuant to the
      employee benefit plans described herein.

(2)   Calculated solely for the purpose of this offering under Rule 457(h) of
      the Securities Act, on the basis of the average of the high and low
      selling prices per share of Common Stock on May 12, 1998 as reported on
      the Nasdaq National Market.


================================================================================


                                       2
<PAGE>   3
                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3. INFORMATION INCORPORATED BY REFERENCE.

      The following documents and information previously filed with the
Securities and Exchange Commission are hereby incorporated by reference:

            (a)   The Registrant's Annual Report on Form 10-K for the year ended
      December 31, 1997 filed pursuant to Section 13 of the Securities Exchange
      Act of 1934 (the "Exchange Act").

            (b)   The Registrant's Quarterly Report on Form 10-Q for the quarter
      ended March 31, 1998 filed pursuant to Section 13 of the Exchange Act.

            (c)   The description of the Common Stock of the Registrant that is
      contained in the Registration Statement on Form 8-A/A filed pursuant to
      Section 12 of the Exchange Act on November 13, 1995.

            (d)   All documents filed by the Registrant pursuant to Sections
      13(a), 13(c), 14 and 15(d) of the Exchange Act subsequent to the filing of
      this Registration Statement and prior to the filing of a post-effective
      amendment which indicates that all securities offered have been sold or
      which deregisters all securities then remaining unsold, shall be deemed to
      be incorporated by reference in the Registration Statement and to be a
      part hereof from the date of filing of such documents.

ITEM 4. DESCRIPTION OF SECURITIES.

      Not applicable.

ITEM 5. INTERESTS OF NAMED EXPERTS AND COUNSEL.

      Not applicable.

ITEM 6. INDEMNIFICATION OF DIRECTORS AND OFFICERS.

      The Registrant has adopted provisions in its Certificate of Incorporation
that eliminate the personal liability of its directors and officers for monetary
damages arising from a breach of their fiduciary duties in certain circumstances
to the fullest extent permitted by law and authorizes the Registrant to
indemnify its directors and officers to the fullest extent permitted by law.
Such limitation of liability does not affect the availability of equitable
remedies such as injunctive relief or rescission.

      The Registrant's Bylaws provide that the Registrant shall indemnify its
directors and officers to the fullest extent permitted by the General
Corporation Law of Delaware, including circumstances in which indemnification is
otherwise discretionary under Delaware law. Section 145 of the General
Corporation Law of Delaware provides for the indemnification of officers,
directors and other corporate agents in terms sufficiently broad to indemnify
such persons, under certain circumstances, for certain liabilities (including
reimbursement of expenses incurred) arising under the Securities Act of 1933.
The Registrant has entered into indemnification agreements to such effect with
its officers and directors containing provisions which are in some respects
broader than the specific indemnification provisions contained in the General
Corporation Law of Delaware. The indemnification agreements may require the
Company, among other things, to indemnify such officers and directors against
certain liabilities that may arise by reason of their status or service as
directors or officers (other than liabilities arising from willful misconduct of
a culpable nature) and to advance their expenses incurred as a result of any
proceeding against them as to which they could be indemnified. The form of such
indemnification agreement has been approved by the Company's stockholders.


                                       3
<PAGE>   4
ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED.

      Not applicable.

ITEM 8. EXHIBITS.

<TABLE>
 EXHIBIT
 NUMBER                              DESCRIPTION
 -------                             -----------

<S>       <C>                                                                  
   5.1    Opinion of Wilson Sonsini Goodrich & Rosati, P.C., as to the legality
          of securities being registered
   10.1   1995 Stock Plan (previously filed as Exhibit 10.1 to Form S-8
          Registration Statement No. 333-23999)
   23.1   Consent of Arthur Andersen LLP, Independent Public Accountants
   23.2   Consent of Wilson Sonsini Goodrich & Rosati, P.C. (contained in
          Exhibit 5.1.hereto)
   24.1   Power of Attorney (see page 6)
</TABLE>

ITEM 9.        UNDERTAKINGS.

      (a)   The undersigned Registrant 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, 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.

            (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.

      (b)   The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
Registrant's annual report pursuant to section 13(a) or section 15(d) of the
Securities Exchange Act of 1934 (and, where applicable, each filing of an
employee benefit plan's annual report pursuant to Section 15(d) of the Exchange
Act) 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
an initial bona fide offering thereof.

      (c)   Insofar as indemnification for liabilities arising under the
Securities Act may be permitted to directors, officers and controlling persons
of the Registrant pursuant to the foregoing provisions, or otherwise, the
Registrant has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the
Securities Act and is, therefore, unenforceable. In the event that a claim for
indemnification against such liabilities (other than the payment by the
Registrant of expenses incurred or paid by a director, officer or controlling
person of the 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, the 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 Securities
Act and will be governed by the final adjudication of such issue.


                                       4
<PAGE>   5
                                   SIGNATURES

      Pursuant to the requirements of the Securities Act, 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 Santa Clara, State of California on May 15, 1998.

                                       VISX, INCORPORATED

                                       By:  /s/   MARK B. LOGAN
                                            ------------------------------------
                                       Mark B. Logan, Chairman of the Board,
                                       President and Chief Executive Officer

                                       By:  /s/   TIMOTHY R. MAIER
                                            ------------------------------------
                                       Timothy R. Maier, Vice President and
                                       Chief Financial Officer


                                       5
<PAGE>   6
                                POWER OF ATTORNEY

      KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature
appears below constitutes and appoints Mark B. Logan and Timothy R. Maier,
jointly and severally, his or her attorneys-in-fact, each with the power of
substitution, for him or her in any and all capacities, to sign any amendments
to this Registration Statement on Form S-8, and to file the same, with exhibits
thereto and other documents in connection therewith, with the Securities and
Exchange Commission, hereby ratifying and confirming all that each of said
attorneys-in-fact, or his substitute or substitutes, may do or cause to be done
by virtue hereof.

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

<TABLE>
<CAPTION>
                 SIGNATURE                             TITLE                              DATE
<S>                                          <C>                                     <C> 


/s/      MARK B. LOGAN                       Chairman of the Board, President        May 15, 1998
-----------------------------------------    and Chief Executive Officer 
         Mark B. Logan                       (Principal Executive        
                                             Officer)*                   
                                             

/s/      TIMOTHY R. MAIER                    Vice President and                      May 15, 1998
-----------------------------------------    Chief Financial Officer     
         Timothy R. Maier                    (Principal Financial and    
                                             Accounting Officer)         
                                             

/s/      ELIZABETH H. DaVILA                 Executive Vice President, Chief         May 15, 1998
-----------------------------------------    Operating Officer and Director*
         Elizabeth H. Davila                 

/s/      GLENDON E. FRENCH                   Director*                               May 15, 1998
-----------------------------------------
         Glendon E. French

/s/      JOHN W. GALIARDO                    Director*                               May 15, 1998
-----------------------------------------
         John W. Galiardo

/s/      RICHARD B. SAYFORD                  Director*                               May 15, 1998
-----------------------------------------
         Richard B. Sayford
</TABLE>

----------


* The employee benefit plan being registered pursuant to this Registration
Statement is subject to administration by the Board of Directors of the
Registrant.


                                       6
<PAGE>   7
<TABLE>
 EXHIBIT
 NUMBER                              DESCRIPTION
 -------                             -----------

<S>       <C>                                                                  
   5.1    Opinion of Wilson Sonsini Goodrich & Rosati, P.C., as to the legality
          of securities being registered
   10.1   1995 Stock Plan (previously filed as Exhibit 10.1 to Form S-8
          Registration Statement No. 333-23999)
   23.1   Consent of Arthur Andersen LLP, Independent Public Accountants
   23.2   Consent of Wilson Sonsini Goodrich & Rosati, P.C. (contained in
          Exhibit 5.1.hereto)
   24.1   Power of Attorney (see page 6)
</TABLE>


                                       7
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 15632}]
{"company-data": {"conformed-name": "VISX INC", "cik": "0000837991", "assigned-sic": "3845", "irs-number": "061161793", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-53041", "film-number": "98628078"}, "business-address": {"street1": "3400 CENTRAL EXPRESSWAY", "city": "SANTA CLARA", "state": "CA", "zip": "95051", "phone": "4087332020"}, "mail-address": {"street1": "VISX INC", "street2": "3400 CENTRAL EXPRESSWAY", "city": "SANTA CLARA", "state": "CA", "zip": "95051-0703"}, "former-company": {"former-conformed-name": "TAUNTON TECHNOLOGIES INC", "date-changed": "19901212"}}
1
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 19, 1998
                                                     REGISTRATION NO. 333-

================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM S-8

                             REGISTRATION STATEMENT
                                      UNDER
                     THE SECURITIES ACT OF 1933, AS AMENDED

                               VISX, INCORPORATED
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
DELAWARE                                              06-1161793
(STATE OR OTHER JURISDICTION OF INCORPORATION              (I.R.S. EMPLOYER IDENTIFICATION NO.)
              OR ORGANIZATION)
3400 CENTRAL EXPRESSWAY
                          SANTA CLARA, CALIFORNIA 95051
                    (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)

                                 1995 STOCK PLAN

                            (FULL TITLE OF THE PLAN)

                                  MARK B. LOGAN
          CHAIRMAN OF THE BOARD, PRESIDENT AND CHIEF EXECUTIVE OFFICER
                               VISX, INCORPORATED
                             3400 CENTRAL EXPRESSWAY
                          SANTA CLARA, CALIFORNIA 95051
            (NAME, ADDRESS AND TELEPHONE NUMBER OF AGENT FOR SERVICE)

                                   COPIES TO:
                             KATRINA J. CHURCH, ESQ.
                               VISX, INCORPORATED
                             3400 CENTRAL EXPRESSWAY
                          SANTA CLARA, CALIFORNIA 95051
                                 (408) 733-2020
2
                         CALCULATION OF REGISTRATION FEE
====================================================================================================================================
                                                                       PROPOSED MAXIMUM       PROPOSED MAXIMUM
TITLE OF SECURITIES TO BE REGISTERED(1)              AMOUNT TO BE       OFFERING PRICE       AGGREGATE OFFERING        AMOUNT OF
                                                      REGISTERED           PER SHARE              PRICE(2)          REGISTRATION FEE
------------------------------------------------------------------------------------------------------------------------------------
1995 Stock Plan
  Common Stock, $0.01 par value..................         455,204           $43.19              $19,660,260.76          $5,799.78
------------------------------------------------------------------------------------------------------------------------------------
====================================================================================================================================
(1)   In addition, pursuant to Rule 416(c) under the Securities Act of 1933, as
      amended (the "Securities Act"), this Registration Statement also covers an
      indeterminate amount of interests to be offered or sold pursuant to the
      employee benefit plans described herein.

(2)   Calculated solely for the purpose of this offering under Rule 457(h) of
      the Securities Act, on the basis of the average of the high and low
      selling prices per share of Common Stock on May 12, 1998 as reported on
      the Nasdaq National Market.

================================================================================

                                       2
3
                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3. INFORMATION INCORPORATED BY REFERENCE.

      The following documents and information previously filed with the
Securities and Exchange Commission are hereby incorporated by reference:

            (a)   The Registrant's Annual Report on Form 10-K for the year ended
      December 31, 1997 filed pursuant to Section 13 of the Securities Exchange
      Act of 1934 (the "Exchange Act").

            (b)   The Registrant's Quarterly Report on Form 10-Q for the quarter
      ended March 31, 1998 filed pursuant to Section 13 of the Exchange Act.

            (c)   The description of the Common Stock of the Registrant that is
      contained in the Registration Statement on Form 8-A/A filed pursuant to
      Section 12 of the Exchange Act on November 13, 1995.

            (d)   All documents filed by the Registrant pursuant to Sections
      13(a), 13(c), 14 and 15(d) of the Exchange Act subsequent to the filing of
      this Registration Statement and prior to the filing of a post-effective
      amendment which indicates that all securities offered have been sold or
      which deregisters all securities then remaining unsold, shall be deemed to
      be incorporated by reference in the Registration Statement and to be a
      part hereof from the date of filing of such documents.

ITEM 4. DESCRIPTION OF SECURITIES.

      Not applicable.

ITEM 5. INTERESTS OF NAMED EXPERTS AND COUNSEL.

      Not applicable.

ITEM 6. INDEMNIFICATION OF DIRECTORS AND OFFICERS.

      The Registrant has adopted provisions in its Certificate of Incorporation
that eliminate the personal liability of its directors and officers for monetary
damages arising from a breach of their fiduciary duties in certain circumstances
to the fullest extent permitted by law and authorizes the Registrant to
indemnify its directors and officers to the fullest extent permitted by law.
Such limitation of liability does not affect the availability of equitable
remedies such as injunctive relief or rescission.

      The Registrant's Bylaws provide that the Registrant shall indemnify its
directors and officers to the fullest extent permitted by the General
Corporation Law of Delaware, including circumstances in which indemnification is
otherwise discretionary under Delaware law. Section 145 of the General
Corporation Law of Delaware provides for the indemnification of officers,
directors and other corporate agents in terms sufficiently broad to indemnify
such persons, under certain circumstances, for certain liabilities (including
reimbursement of expenses incurred) arising under the Securities Act of 1933.
The Registrant has entered into indemnification agreements to such effect with
its officers and directors containing provisions which are in some respects
broader than the specific indemnification provisions contained in the General
Corporation Law of Delaware. The indemnification agreements may require the
Company, among other things, to indemnify such officers and directors against
certain liabilities that may arise by reason of their status or service as
directors or officers (other than liabilities arising from willful misconduct of
a culpable nature) and to advance their expenses incurred as a result of any
proceeding against them as to which they could be indemnified. The form of such
indemnification agreement has been approved by the Company's stockholders.

                                       3
4
ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED.

      Not applicable.

ITEM 8. EXHIBITS.

 EXHIBIT
 NUMBER                              DESCRIPTION
 -------                             -----------
5.1    Opinion of Wilson Sonsini Goodrich & Rosati, P.C., as to the legality
          of securities being registered
   10.1   1995 Stock Plan (previously filed as Exhibit 10.1 to Form S-8
          Registration Statement No. 333-23999)
   23.1   Consent of Arthur Andersen LLP, Independent Public Accountants
   23.2   Consent of Wilson Sonsini Goodrich & Rosati, P.C. (contained in
          Exhibit 5.1.hereto)
   24.1   Power of Attorney (see page 6)
ITEM 9.        UNDERTAKINGS.

      (a)   The undersigned Registrant 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, 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.

            (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.

      (b)   The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
Registrant's annual report pursuant to section 13(a) or section 15(d) of the
Securities Exchange Act of 1934 (and, where applicable, each filing of an
employee benefit plan's annual report pursuant to Section 15(d) of the Exchange
Act) 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
an initial bona fide offering thereof.

      (c)   Insofar as indemnification for liabilities arising under the
Securities Act may be permitted to directors, officers and controlling persons
of the Registrant pursuant to the foregoing provisions, or otherwise, the
Registrant has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the
Securities Act and is, therefore, unenforceable. In the event that a claim for
indemnification against such liabilities (other than the payment by the
Registrant of expenses incurred or paid by a director, officer or controlling
person of the 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, the 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 Securities
Act and will be governed by the final adjudication of such issue.

                                       4
5
                                   SIGNATURES

      Pursuant to the requirements of the Securities Act, 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 Santa Clara, State of California on May 15, 1998.

                                       VISX, INCORPORATED

                                       By:  /s/   MARK B. LOGAN
                                            ------------------------------------
                                       Mark B. Logan, Chairman of the Board,
                                       President and Chief Executive Officer

                                       By:  /s/   TIMOTHY R. MAIER
                                            ------------------------------------
                                       Timothy R. Maier, Vice President and
                                       Chief Financial Officer

                                       5
6
                                POWER OF ATTORNEY

      KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature
appears below constitutes and appoints Mark B. Logan and Timothy R. Maier,
jointly and severally, his or her attorneys-in-fact, each with the power of
substitution, for him or her in any and all capacities, to sign any amendments
to this Registration Statement on Form S-8, and to file the same, with exhibits
thereto and other documents in connection therewith, with the Securities and
Exchange Commission, hereby ratifying and confirming all that each of said
attorneys-in-fact, or his substitute or substitutes, may do or cause to be done
by virtue hereof.

      Pursuant to the requirements of the Securities Act, this Registration
Statement has been signed by the following persons in the capacities and on the
date indicated.
SIGNATURE                             TITLE                              DATE
/s/      MARK B. LOGAN                       Chairman of the Board, President        May 15, 1998
-----------------------------------------    and Chief Executive Officer 
         Mark B. Logan                       (Principal Executive        
                                             Officer)*                   
                                             

/s/      TIMOTHY R. MAIER                    Vice President and                      May 15, 1998
-----------------------------------------    Chief Financial Officer     
         Timothy R. Maier                    (Principal Financial and    
                                             Accounting Officer)         
                                             

/s/      ELIZABETH H. DaVILA                 Executive Vice President, Chief         May 15, 1998
-----------------------------------------    Operating Officer and Director*
         Elizabeth H. Davila                 

/s/      GLENDON E. FRENCH                   Director*                               May 15, 1998
-----------------------------------------
         Glendon E. French

/s/      JOHN W. GALIARDO                    Director*                               May 15, 1998
-----------------------------------------
         John W. Galiardo

/s/      RICHARD B. SAYFORD                  Director*                               May 15, 1998
-----------------------------------------
         Richard B. Sayford
----------

* The employee benefit plan being registered pursuant to this Registration
Statement is subject to administration by the Board of Directors of the
Registrant.

                                       6
7

 EXHIBIT
 NUMBER                              DESCRIPTION
 -------                             -----------
5.1    Opinion of Wilson Sonsini Goodrich & Rosati, P.C., as to the legality
          of securities being registered
   10.1   1995 Stock Plan (previously filed as Exhibit 10.1 to Form S-8
          Registration Statement No. 333-23999)
   23.1   Consent of Arthur Andersen LLP, Independent Public Accountants
   23.2   Consent of Wilson Sonsini Goodrich & Rosati, P.C. (contained in
          Exhibit 5.1.hereto)
   24.1   Power of Attorney (see page 6)
7