Document:

<PAGE>
                                                                   Exhibit 10.33

                         NUMERICAL TECHNOLOGIES, INC.

       AMENDMENT NO. 1 TO LARS HERLITZ'S STOCK OPTION AGREEMENTS DATED
                    FEBRUARY 3, 1999 AND DECEMBER 27, 1999

     This Agreement is made as of January 24, 2000 by and among Numerical
Technologies, Inc., a California corporation (the "Company"), and Lars Herlitz
("Herlitz").

     WHEREAS, the Company and Herlitz are parties to Stock Option Agreements -
Early Exercise dated February 3, 1999 and December 27, 1999 (individually, an
"Option Agreement" and collectively, the "Option Agreements"), pursuant to which
Herlitz was granted options purchase 115,000 shares and 55,000 shares,
respectively, of the Company's Common Stock.

     WHEREAS, on January 24, 2000, the Board of Directors of the Company
approved amendments to the Option Agreements to (i) provide for payment of the
exercise price by, among other methods, promissory note and (ii) add a section
entitled "Change of Control; Constructive Termination", which shall provide for
accelerated vesting in the event of a change of control of the Company or in
connection with "involuntary termination" of employment of such individuals
following a change of control.

     NOW, THEREFORE, in consideration of the foregoing, the parties agree as
follows:

                                   AGREEMENT

     1.  Amendment to Option Agreements.  The following paragraphs are hereby
         ------------------------------
inserted into Part I of each Option Agreement, between the paragraphs entitled
"Exercise and Vesting Schedule" and "Termination Period".

     "Change of Control; Constructive Termination:
      -------------------------------------------

     Notwithstanding the provisions of Section 12(c) of the Plan, if the Company
merges with or into another entity, sells all or substantially all of its
assets, or enters into any other similar transaction or reorganization
(including without limitation, a sale of stock of the Company) as a result of
which the shareholders of the Company immediately prior to such transaction will
not hold at least 50% of the voting power of the surviving, purchasing or
continuing entity, as applicable (taking into account any securities issued to
the shareholders of the Company in the transaction) (a "Change of Control
Transaction"), then on the six month anniversary of the Change of Control
Transaction (the "Anniversary Date") fifty percent (50%) of the Shares subject
to the Option which have not vested as of the Anniversary Date shall become
fully vested and exercisable. The Board shall notify the Optionee at least
fifteen (15) days prior to the closing of a Change of Control Transaction, and
such notification shall include a statement as to whether or not the Option will
be assumed by the surviving or purchasing entity or whether an equivalent
substitute option will be provided by such entity.

     Following an assumption or substitution of the Option in connection with a
Change of Control Transaction, if the Optionee's status as an Employee of the
successor corporation is terminated by the successor corporation as a result of
an Involuntary Termination (as defined below) within twelve months
<PAGE>

following the Change of Control Transaction, the Optionee shall fully vest in
and have the right to exercise the Option as to all of the Shares, including
Shares as to which the Option would not otherwise be vested or exercisable.

     Any of the following events shall constitute an "Involuntary Termination":
(i) without the Optionee's express written consent, a significant reduction of
the Optionee's duties, authority and responsibilities, relative to the
Optionee's duties, authority and responsibilities as in effect immediately prior
to the Change of Control Transaction; (ii) a material reduction in the base
salary of the Optionee as in effect immediately prior to the Change of Control
Transaction; (iii) a material reduction in the kind or level of employee
benefits, including bonuses, to which the Optionee was entitled immediately
prior to the Change of Control Transaction with the result that the Optionee's
overall benefits package is significantly reduced; (iv) the relocation of the
Optionee to a facility or a location more than sixty (60) miles from the
Optionee's then present location, without the Optionee's express written
consent; (v) any purported termination of the Optionee which is not effected for
Disability or for Cause (as defined below), or any purported termination for
which the grounds relied upon are not valid; (vi) or any act or set of facts or
circumstances which would, under California case law or statute, constitute a
constructive termination of the Optionee.

     "Cause" shall mean (i) any act of personal dishonesty taken by the Optionee
in connection with his responsibilities as a Service Provider and intended to
result in substantial personal enrichment of the Optionee, (ii) Optionee's
conviction of a felony, (iii) a willful act by the Optionee which constitutes
gross misconduct and which is injurious to the Successor Corporation, and (iv)
following delivery to the Optionee of a written demand for performance from the
Successor Corporation which describes the basis for the Successor Corporation's
belief that the Optionee has not substantially performed his duties, continued
violations by the Optionee of the Optionee's obligations to the Successor
Corporation which are demonstrably willful and deliberate on the Optionee's
part."

     2.   Amendment to Option Agreement re Payment by Note.  The following
          ------------------------------------------------
subparagraph (e) is hereby added to Section 5 of each Option Agreement.

          "(e)  with the Administrator's consent, delivery of Optionee's
promissory note (the "Note") in the form attached hereto as Exhibit D, in the
amount of the aggregate Exercise Price of the Exercised Shares together with the
execution and delivery by the Optionee of the Security Agreement attached hereto
as Exhibit E. The Note shall bear interest at the "applicable federal rate"
prescribed under the Code and its regulations at time of purchase, and shall be
secured by a pledge of the Shares purchased by the Note pursuant to the Security
Agreement."

     3.   Amendment to Option Agreement re Form of Note and Form of Security
          ------------------------------------------------------------------
Agreement.  The form of Note attached hereto as Attachment 1 and the form of
---------
Security Agreement attached hereto as Attachment 2 are hereby added to each of
the Option Agreements as Exhibit D and Exhibit E, respectively.

     4.   Miscellaneous.
          -------------

          4.1. Governing Law. This Agreement shall be governed in all respects
               -------------
by the internal laws of the State of California.

                                      -2-
<PAGE>

          4.2.  Successors and Assigns. Except as otherwise provided herein, the
                ----------------------
provisions hereof shall inure to the benefit of and be binding upon, the
successors, assigns, heirs, executors and administrators of the parties hereto.

          4.3.  Amendment.  Neither this Agreement nor any term hereof may be
                ---------
amended, waived, discharged or terminated other than by written instrument
signed by the party against whom enforcement of such amendment, waiver,
discharge or termination is sought.

          4.4.  Counterparts.  This Agreement may be executed in any number of
                ------------
counterparts, each of which shall be enforceable against the parties actually
executing such counterparts, and all of which together shall constitute one
instrument.

     The foregoing Agreement is hereby executed as of the date first written
above.

                                             "COMPANY"

                                             NUMERICAL TECHNOLOGIES, INC.

                                             By: /s/ Yagyenshu C. Pati
                                                --------------------------------

                                             Title: President & CEO
                                                   -----------------------------

                                             "HERLITZ"

                                             /s/ Lars Herlitz
                                             ___________________________________
                                             Lars Herlitz

                                      -3-
<PAGE>

                                 ATTACHMENT 1
                                 ------------

                                   EXHIBIT D

                                     NOTE

$____________                                               San Jose, California

____________, 20___

     FOR VALUE RECEIVED, _____________________ promises to pay to Numerical
Technologies, Inc., a California corporation (the "Company"), or order, the
principal sum of ____________________________________ ($_________), together
with interest on the unpaid principal hereof from the date hereof at the rate of
____% per annum, compounded annually.

     Principal and interest shall be due and payable on ______________, 20___.
Payment of principal and interest shall be made in lawful money of the United
States of America.

     The undersigned may at any time prepay all or any portion of the principal
or interest owing hereunder.

     This Note is subject to the terms of the Option, dated as of ________,
1999. This Note is secured in part by a pledge of the Company's Common Stock
under the terms of a Security Agreement of even date herewith and is subject to
all the provisions thereof.

     The holder of this Note shall have full recourse against the undersigned,
and shall not be required to proceed against the collateral securing this Note
in the event of default.

     In the event the undersigned shall cease to be an employee, director or
consultant of the Company for any reason, this Note shall, at the option of the
Company, be accelerated, and the whole unpaid balance on this Note of principal
and accrued interest shall be immediately due and payable.

     Should any action be instituted for the collection of this Note, the
reasonable costs and attorneys' fees therein of the holder shall be paid by the
undersigned.

                                              _________________________________
<PAGE>

                                  ATTACHMENT 2
                                  ------------

                                   EXHIBIT E

                               SECURITY AGREEMENT

     This Security Agreement is made as of ____________, 20___ between Numerical
Technologies, Inc., a California corporation ("Pledgee"), and _________________
("Pledgor").

                                   Recitals
                                   --------

     Pursuant to Pledgor's election to purchase Shares under the Option
Agreement dated _____________, 1999 (the "Option"), between Pledgor and Pledgee
under Pledgee's 1997 Stock Plan, and Pledgor's election under the terms of the
Option to pay for such shares with his promissory note (the "Note"), Pledgor has
purchased _________ shares of Pledgee's Common Stock (the "Shares") at a price
of $_____ per share, for a total purchase price of $__________. The Note and the
obligations thereunder are as set forth in Exhibit D to the Option.

     NOW, THEREFORE, it is agreed as follows:

     A.   Creation and Description of Security Interest.  In consideration
          ---------------------------------------------
of the transfer of the Shares to Pledgor under the Option Agreement, Pledgor,
pursuant to the California Commercial Code, hereby pledges all of such Shares
(herein sometimes referred to as the "Collateral") represented by certificate
number ______, duly endorsed in blank or with executed stock powers, and
herewith delivers said certificate to the Secretary of Pledgee ("Pledgeholder"),
who shall hold said certificate subject to the terms and conditions of this
Security Agreement.

     The pledged stock (together with an executed blank stock assignment for use
in transferring all or a portion of the Shares to Pledgee if, as and when
required pursuant to this Security Agreement) shall be held by the Pledgeholder
as security for the repayment of the Note, and any extensions or renewals
thereof, to be executed by Pledgor pursuant to the terms of the Option, and the
Pledgeholder shall not encumber or dispose of such Shares except in accordance
with the provisions of this Security Agreement.

     B.   Pledgor's Representations and Covenants.  To induce Pledgee to enter
          ---------------------------------------
into this Security Agreement, Pledgor represents and covenants to Pledgee, its
successors and assigns, as follows:

          (A)  Payment of Indebtedness.  Pledgor will pay the principal sum of
               -----------------------
the Note secured hereby, together with interest thereon, at the time and in the
manner provided in the Note.

          (B)  Encumbrances.  The Shares are free of all other encumbrances,
               ------------
defenses and liens, and Pledgor will not further encumber the Shares without the
prior written consent of Pledgee.
<PAGE>

          (C)  Margin Regulations.  In the event that Pledgee's Common Stock is
               ------------------
now or later becomes margin-listed by the Federal Reserve Board and Pledgee is
classified as a "lender" within the meaning of the regulations under Part 207 of
Title 12 of the Code of Federal Regulations ("Regulation G"), Pledgor agrees to
cooperate with Pledgee in making any amendments to the Note or providing any
additional collateral as may be necessary to comply with such regulations.

     C.   Voting Rights.  During the term of this pledge and so long as all
          -------------
payments of principal and interest are made as they become due under the terms
of the Note, Pledgor shall have the right to vote all of the Shares pledged
hereunder.

     D.   Stock Adjustments.  In the event that during the term of the pledge
          -----------------
any stock dividend, reclassification, readjustment or other changes are declared
or made in the capital structure of Pledgee, all new, substituted and additional
shares or other securities issued by reason of any such change shall be
delivered to and held by the Pledgee under the terms of this Security Agreement
in the same manner as the Shares originally pledged hereunder. In the event of
substitution of such securities, Pledgor, Pledgee and Pledgeholder shall
cooperate and execute such documents as are reasonable so as to provide for the
substitution of such Collateral and, upon such substitution, references to
"Shares" in this Security Agreement shall include the substituted shares of
capital stock of Pledgor as a result thereof.

     E.   Options and Rights.  In the event that, during the term of this
          ------------------
pledge, subscription Options or other rights or options shall be issued in
connection with the pledged Shares, such rights, Options and options shall be
the property of Pledgor and, if exercised by Pledgor, all new stock or other
securities so acquired by Pledgor as it relates to the pledged Shares then held
by Pledgeholder shall be immediately delivered to Pledgeholder, to be held under
the terms of this Security Agreement in the same manner as the Shares pledged.

     F.   Default.  Pledgor shall be deemed to be in default of the Note and of
          -------
this Security Agreement in the event:

          (A)  Payment of principal or interest on the Note shall be delinquent
for a period of 10 days or more; or

          (B)  Pledgor fails to perform any of the covenants set forth in the
Option or contained in this Security Agreement for a period of 10 days after
written notice thereof from Pledgee.

     In the case of an event of Default, as set forth above, Pledgee shall have
the right to accelerate payment of the Note upon notice to Pledgor, and Pledgee
shall thereafter be entitled to pursue its remedies under the California
Commercial Code.

     G.   Release of Collateral.  Subject to any applicable contrary rules under
          ---------------------
Regulation G, there shall be released from this pledge a portion of the pledged
Shares held by Pledgeholder hereunder upon payments of the principal of the
Note. The number of the pledged Shares which shall be released shall be that
number of full Shares which bears the same proportion to the initial number of
Shares pledged hereunder as the payment of principal bears to the initial full
principal amount of the Note.

     H.   Withdrawal or Substitution of Collateral.  Pledgor shall not sell,
          ----------------------------------------
withdraw, pledge, substitute or otherwise dispose of all or any part of the
Collateral without the prior written consent of Pledgee.

                                      -2-
<PAGE>

     I.   Term.  The within pledge of Shares shall continue until the payment
          ----
of all indebtedness secured hereby, at which time the remaining pledged stock
shall be promptly delivered to Pledgor, subject to the provisions for prior
release of a portion of the Collateral as provided in paragraph 7 above.

     J.   Insolvency.  Pledgor agrees that if a bankruptcy or insolvency
          ----------
proceeding is instituted by or against it, or if a receiver is appointed for the
property of Pledgor, or if Pledgor makes an assignment for the benefit of
creditors, the entire amount unpaid on the Note shall become immediately due and
payable, and Pledgee may proceed as provided in the case of default.

     K.   Pledgeholder Liability.  In the absence of willful or gross
          ----------------------
negligence, Pledgeholder shall not be liable to any party for any of his acts,
or omissions to act, as Pledgeholder.

     L.   Invalidity of Particular Provisions.  Pledgor and Pledgee agree that
          -----------------------------------
the enforceability or invalidity of any provision or provisions of this Security
Agreement shall not render any other provision or provisions herein contained
unenforceable or invalid.

     M.   Successors or Assigns.  Pledgor and Pledgee agree that all of the
          ---------------------
terms of this Security Agreement shall be binding on their respective successors
and assigns, and that the term "Pledgor" and the term "Pledgee" as used herein
shall be deemed to include, for all purposes, the respective designees,
successors, assigns, heirs, executors and administrators.

     N.   Governing Law.  This Security Agreement shall be interpreted and
          -------------
governed under the internal substantive laws, but not the choice of law rules,
of California.

                                      -3-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the day and year first above written.

     "PLEDGOR"
                               ________________________________________
                               Signature

                               ________________________________________
                               Print Name

                               Address:
                                         _______________________________________

                                         _______________________________________

     "PLEDGEE"                 NUMERICAL TECHNOLOGIES, INC. a California
                               corporation

                               ________________________________________
                               Signature

                               ________________________________________
                               Print Name

                               ________________________________________
                               Title

     "PLEDGEHOLDER"
                               ________________________________________
                               Secretary of Numerical Technologies, Inc.

                                      -4-<PAGE>
                                                                  Exhibit 10.34

                         NUMERICAL TECHNOLOGIES, INC.

AMENDMENT NO. 1 TO ATUL SHARAN'S STOCK OPTION AGREEMENTS DATED OCTOBER 23, 1998,
                     MARCH 31, 1999 AND DECEMBER 27, 1999

     This Agreement is made as of January 24, 2000 by and among Numerical
Technologies, Inc., a California corporation (the "Company"), and Atul Sharan
("Sharan").

     WHEREAS, the Company and Sharan are parties to Stock Option Agreements -
Early Exercise dated October 23, 1998, March 31, 1999 and December 27, 1999
(individually, an "Option Agreement" and collectively, the "Option Agreements"),
pursuant to which Sharan was granted options purchase 90,000 shares, 60,000 and
125,000 shares, respectively, of the Company's Common Stock.

     WHEREAS, on January 24, 2000, the Board of Directors of the Company
approved amendments to the Option Agreements to (i) provide for payment of the
exercise price by, among other methods, promissory note and (ii) add a section
entitled "Change of Control; Constructive Termination", which shall provide for
accelerated vesting in the event of a change of control of the Company or in
connection with "involuntary termination" of employment of such individuals
following a change of control.

     NOW, THEREFORE, in consideration of the foregoing, the parties agree as
follows:

                                   AGREEMENT

     1.   Amendment to Option Agreements.  The following paragraphs are hereby
          ------------------------------
inserted into Part I of each Option Agreement, between the paragraphs entitled
"Exercise and Vesting Schedule" and  "Termination Period".

     "Change of Control; Constructive Termination:
      -------------------------------------------

     Notwithstanding the provisions of Section 12(c) of the Plan, if the Company
merges with or into another entity, sells all or substantially all of its
assets, or enters into any other similar transaction or reorganization
(including without limitation, a sale of stock of the Company) as a result of
which the shareholders of the Company immediately prior to such transaction will
not hold at least 50% of the voting power of the surviving, purchasing or
continuing entity, as applicable (taking into account any securities issued to
the shareholders of the Company in the transaction) (a "Change of Control
Transaction"), then on the six month anniversary of the Change of Control
Transaction (the "Anniversary Date") fifty percent (50%) of the Shares subject
to the Option which have not vested as of the Anniversary Date shall become
fully vested and exercisable.  The Board shall notify the Optionee at least
fifteen (15) days prior to the closing of a Change of Control Transaction, and
such notification shall include a statement as to whether or not the Option will
be assumed by the surviving or purchasing entity or whether an equivalent
substitute option will be provided by such entity.

     Following an assumption or substitution of the Option in connection with a
Change of Control Transaction, if the Optionee's status as an Employee of the
successor corporation is terminated by the successor corporation as a result of
an Involuntary Termination (as defined below) within twelve months
<PAGE>

following the Change of Control Transaction, the Optionee shall fully vest in
and have the right to exercise the Option as to all of the Shares, including
Shares as to which the Option would not otherwise be vested or exercisable.

     Any of the following events shall constitute an "Involuntary Termination":
(i) without the Optionee's express written consent, a significant reduction of
the Optionee's duties, authority and responsibilities, relative to the
Optionee's duties, authority and responsibilities as in effect immediately prior
to the Change of Control Transaction; (ii) a material reduction in the base
salary of the Optionee as in effect immediately prior to the Change of Control
Transaction; (iii) a material reduction in the kind or level of employee
benefits, including bonuses, to which the Optionee was entitled immediately
prior to the Change of Control Transaction with the result that the Optionee's
overall benefits package is significantly reduced; (iv) the relocation of the
Optionee to a facility or a location more than sixty (60) miles from the
Optionee's then present location, without the Optionee's express written
consent; (v) any purported termination of the Optionee which is not effected for
Disability or for Cause (as defined below), or any purported termination for
which the grounds relied upon are not valid; (vi) or any act or set of facts or
circumstances which would, under California case law or statute, constitute a
constructive termination of the Optionee.

     "Cause" shall mean (i) any act of personal dishonesty taken by the Optionee
in connection with his responsibilities as a Service Provider and intended to
result in substantial personal enrichment of the Optionee, (ii) Optionee's
conviction of a felony, (iii) a willful act by the Optionee which constitutes
gross misconduct and which is injurious to the Successor Corporation, and (iv)
following delivery to the Optionee of a written demand for performance from the
Successor Corporation which describes the basis for the Successor Corporation's
belief that the Optionee has not substantially performed his duties, continued
violations by the Optionee of the Optionee's obligations to the Successor
Corporation which are demonstrably willful and deliberate on the Optionee's
part."

     2.   Amendment to Option Agreement re Payment by Note.  The following
          ------------------------------------------------
subparagraph (e) is hereby added to Section 5 of each Option Agreement.

          "(e)  with the Administrator's consent, delivery of Optionee's
promissory note (the "Note") in the form attached hereto as Exhibit D, in the
amount of the aggregate Exercise Price of the Exercised Shares together with the
execution and delivery by the Optionee of the Security Agreement attached hereto
as Exhibit E. The Note shall bear interest at the "applicable federal rate"
prescribed under the Code and its regulations at time of purchase, and shall be
secured by a pledge of the Shares purchased by the Note pursuant to the Security
Agreement."

     3.   Amendment to Option Agreement re Form of Note and Form of Security
          ------------------------------------------------------------------
Agreement.  The form of Note attached hereto as Attachment 1 and the form of
---------
Security Agreement attached hereto as Attachment 2 are hereby added to each of
the Option Agreements as Exhibit D and Exhibit E, respectively.

     4.   Miscellaneous.
          -------------

          4.1.  Governing Law.  This Agreement shall be governed in all
                -------------
respects by the internal laws of the State of California.

                                      -2-
<PAGE>

          4.2. Successors and Assigns.  Except as otherwise provided herein, the
               ----------------------
provisions hereof shall inure to the benefit of and be binding upon, the
successors, assigns, heirs, executors and administrators of the parties hereto.

          4.3. Amendment.  Neither this Agreement nor any term hereof may be
               ---------
amended, waived, discharged or terminated other than by written instrument
signed by the party against whom enforcement of such amendment, waiver,
discharge or termination is sought.

          4.4. Counterparts.  This Agreement may be executed in any number of
               ------------
counterparts, each of which shall be enforceable against the parties actually
executing such counterparts, and all of which together shall constitute one
instrument.

     The foregoing Agreement is hereby executed as of the date first written
above.

                                             "COMPANY"

                                             NUMERICAL TECHNOLOGIES, INC.

                                             By: /s/ Yagyensh C. Pati
                                                 _______________________________

                                             Title: President & CEO
                                                    ____________________________

                                             "SHARAN"

                                             /s/ Atul Sharan
                                             __________________________________
                                             Atul Sharan

                                      -3-
<PAGE>

                                 ATTACHMENT 1
                                 ------------

                                   EXHIBIT D

                                     NOTE

$____________                                               San Jose, California

____________, 20___

          FOR VALUE RECEIVED, _____________________ promises to pay to Numerical
Technologies, Inc., a California corporation (the "Company"), or order, the
principal sum of ____________________________________ ($_________), together
with interest on the unpaid principal hereof from the date hereof at the rate of
____% per annum, compounded annually.

          Principal and interest shall be due and payable on ______________,
20___.  Payment of principal and interest shall be made in lawful money of the
United States of America.

          The undersigned may at any time prepay all or any portion of the
principal or interest owing hereunder.

          This Note is subject to the terms of the Option, dated as of
______________, 1999.  This Note is secured in part by a pledge of the Company's
Common Stock under the terms of a Security Agreement of even date herewith and
is subject to all the provisions thereof.

          The holder of this Note shall have full recourse against the
undersigned, and shall not be required to proceed against the collateral
securing this Note in the event of default.

          In the event the undersigned shall cease to be an employee, director
or consultant of the Company for any reason, this Note shall, at the option of
the Company, be accelerated, and the whole unpaid balance on this Note of
principal and accrued interest shall be immediately due and payable.

          Should any action be instituted for the collection of this Note, the
reasonable costs and attorneys' fees therein of the holder shall be paid by the
undersigned.

                                            ____________________________________
<PAGE>

                                 ATTACHMENT 2
                                 ------------

                                   EXHIBIT E

                              SECURITY AGREEMENT

          This Security Agreement is made as of ____________, 20___ between
Numerical Technologies, Inc., a California corporation ("Pledgee"), and
_________________ ("Pledgor").

                                   Recitals
                                   --------

          Pursuant to Pledgor's election to purchase Shares under the Option
Agreement dated _____________, 1999 (the "Option"), between Pledgor and Pledgee
under Pledgee's 1997 Stock Plan, and Pledgor's election under the terms of the
Option to pay for such shares with his promissory note (the "Note"), Pledgor has
purchased _________ shares of Pledgee's Common Stock (the "Shares") at a price
of $_____  per share, for a total purchase price of $__________.  The Note and
the obligations thereunder are as set forth in Exhibit D to the Option.

          NOW, THEREFORE, it is agreed as follows:

          A.  Creation and Description of Security Interest.  In consideration
              ---------------------------------------------
of the transfer of the Shares to Pledgor under the Option Agreement, Pledgor,
pursuant to the California Commercial Code, hereby pledges all of such Shares
(herein sometimes referred to as the "Collateral") represented by certificate
number ______, duly endorsed in blank or with executed stock powers, and
herewith delivers said certificate to the Secretary of Pledgee ("Pledgeholder"),
who shall hold said certificate subject to the terms and conditions of this
Security Agreement.

          The pledged stock (together with an executed blank stock assignment
for use in transferring all or a portion of the Shares to Pledgee if, as and
when required pursuant to this Security Agreement) shall be held by the
Pledgeholder as security for the repayment of the Note, and any extensions or
renewals thereof, to be executed by Pledgor pursuant to the terms of the Option,
and the Pledgeholder shall not encumber or dispose of such Shares except in
accordance with the provisions of this Security Agreement.

          B.  Pledgor's Representations and Covenants.  To induce Pledgee to
              ---------------------------------------
enter into this Security Agreement, Pledgor represents and covenants to Pledgee,
its successors and assigns, as follows:

              (A) Payment of Indebtedness.  Pledgor will pay the principal sum
                  -----------------------
of the Note secured hereby, together with interest thereon, at the time and in
the manner provided in the Note.

              (B) Encumbrances.  The Shares are free of all other encumbrances,
              ------------
defenses and liens, and Pledgor will not further encumber the Shares without the
prior written consent of Pledgee.
<PAGE>

              (C) Margin Regulations.  In the event that Pledgee's Common
                  ------------------
Stock is now or later becomes margin-listed by the Federal Reserve Board and
Pledgee is classified as a "lender" within the meaning of the regulations under
Part 207 of Title 12 of the Code of Federal Regulations ("Regulation G"),
Pledgor agrees to cooperate with Pledgee in making any amendments to the Note or
providing any additional collateral as may be necessary to comply with such
regulations.

          C.  Voting Rights.  During the term of this pledge and so long as all
              -------------
payments of principal and interest are made as they become due under the terms
of the Note, Pledgor shall have the right to vote all of the Shares pledged
hereunder.

          D.  Stock Adjustments.  In the event that during the term of the
              -----------------
pledge any stock dividend, reclassification, readjustment or other changes are
declared or made in the capital structure of Pledgee, all new, substituted and
additional shares or other securities issued by reason of any such change shall
be delivered to and held by the Pledgee under the terms of this Security
Agreement in the same manner as the Shares originally pledged hereunder.  In the
event of substitution of such securities, Pledgor, Pledgee and Pledgeholder
shall cooperate and execute such documents as are reasonable so as to provide
for the substitution of such Collateral and, upon such substitution, references
to "Shares" in this Security Agreement shall include the substituted shares of
capital stock of Pledgor as a result thereof.

          E.  Options and Rights.  In the event that, during the term of this
              ------------------
pledge, subscription Options or other rights or options shall be issued in
connection with the pledged Shares, such rights, Options and options shall be
the property of Pledgor and, if exercised by Pledgor, all new stock or other
securities so acquired by Pledgor as it relates to the pledged Shares then held
by Pledgeholder shall be immediately delivered to Pledgeholder, to be held under
the terms of this Security Agreement in the same manner as the Shares pledged.

          F.  Default.  Pledgor shall be deemed to be in default of the Note and
              -------
of this Security Agreement in the event:

              (A) Payment of principal or interest on the Note shall be
delinquent for a period of 10 days or more; or

              (B) Pledgor fails to perform any of the covenants set forth in the
Option or contained in this Security Agreement for a period of 10 days after
written notice thereof from Pledgee.

          In the case of an event of Default, as set forth above, Pledgee shall
have the right to accelerate payment of the Note upon notice to Pledgor, and
Pledgee shall thereafter be entitled to pursue its remedies under the California
Commercial Code.

          G.  Release of Collateral.  Subject to any applicable contrary rules
              ---------------------
under Regulation G, there shall be released from this pledge a portion of the
pledged Shares held by Pledgeholder hereunder upon payments of the principal of
the Note.  The number of the pledged Shares which shall be released shall be
that number of full Shares which bears the same proportion to the initial number
of Shares pledged hereunder as the payment of principal bears to the initial
full principal amount of the Note.

          H.  Withdrawal or Substitution of Collateral.  Pledgor shall not sell,
              ----------------------------------------
withdraw, pledge, substitute or otherwise dispose of all or any part of the
Collateral without the prior written consent of Pledgee.

                                      -2-
<PAGE>

          I.  Term.  The within pledge of Shares shall continue until the
              ----
payment of all indebtedness secured hereby, at which time the remaining pledged
stock shall be promptly delivered to Pledgor, subject to the provisions for
prior release of a portion of the Collateral as provided in paragraph 7 above.

          J.  Insolvency.  Pledgor agrees that if a bankruptcy or insolvency
              ----------
proceeding is instituted by or against it, or if a receiver is appointed for the
property of Pledgor, or if Pledgor makes an assignment for the benefit of
creditors, the entire amount unpaid on the Note shall become immediately due and
payable, and Pledgee may proceed as provided in the case of default.

          K.  Pledgeholder Liability.  In the absence of willful or gross
              ----------------------
negligence, Pledgeholder shall not be liable to any party for any of his acts,
or omissions to act, as Pledgeholder.

          L.  Invalidity of Particular Provisions.  Pledgor and Pledgee agree
              -----------------------------------
that the enforceability or invalidity of any provision or provisions of this
Security Agreement shall not render any other provision or provisions herein
contained unenforceable or invalid.

          M.  Successors or Assigns.  Pledgor and Pledgee agree that all of the
              ---------------------
terms of this Security Agreement shall be binding on their respective successors
and assigns, and that the term "Pledgor" and the term "Pledgee" as used herein
shall be deemed to include, for all purposes, the respective designees,
successors, assigns, heirs, executors and administrators.

          N.  Governing Law.  This Security Agreement shall be interpreted and
              -------------
governed under the internal substantive laws, but not the choice of law rules,
of California.

                                      -3-
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the day and year first above written.

          "PLEDGOR"                     _________________________________
                                        Signature

                                        _________________________________
                                        Print Name

                                        Address:  ___________________________

                                                  ___________________________

          "PLEDGEE"                     NUMERICAL TECHNOLOGIES, INC.
                                        a California corporation

                                        ________________________________
                                        Signature

                                        ________________________________
                                        Print Name

                                        ________________________________
                                        Title

          "PLEDGEHOLDER"                ________________________________
                                        Secretary of Numerical Technologies,
                                         Inc.

                                      -4-

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