<PAGE>
 
                                                                    EXHIBIT 10.9

                          BAY VIEW CAPITAL CORPORATION


           AMENDED AND RESTATED 1995 STOCK OPTION AND INCENTIVE PLAN


      1.  Plan Purpose.  The purpose of the Plan is to promote the long-term
          ------------                                                      
interests of the Corporation and its stockholders by providing a means for
attracting and retaining officers and employees of the Corporation and its
Affiliates.  The Plan is intended to be an incentive stock option plan within
the meaning of Section 422 of the Code but not all Options granted hereunder are
required to be Incentive Stock Options.

      2.  Definitions.  The following definitions are applicable to the Plan:
          -----------                                                        

          "Affiliate" -- means any "parent corporation" or "subsidiary
corporation" of the Corporation as such terms are defined in Section 425(e) and
(f), respectively, of the Code.

          "Award" -- means the grant by the Committee of an Incentive Stock
Option, a Non-Qualified Stock Option, a Stock Appreciation Right, a Limited
Stock Appreciation Right, or of Restricted Stock, or any combination thereof, as
provided in the Plan.

          "Code" -- means the Internal Revenue Code of 1986, as amended.

          "Committee" -- means the Committee referred to in Section 3 hereof.

          "Continuous Service" -- shall mean the absence of any interruption or
termination of service as an officer or employee of the Corporation or an
Affiliate, except that when used with respect to persons granted an Incentive
Stock Option means the absence of any interruption or termination of service as
an employee of the Corporation or an Affiliate.  Service shall not be considered
interrupted in the case of sick leave, military leave or any other leave of
absence approved by the Corporation or in the case of transfers between payroll
locations of the Corporation or between the Corporation, its parent, its
subsidiaries or its successor.

          "Corporation" -- means Bay View Capital Corporation, a Delaware
Corporation and any successor thereto.

          "Disinterested Person" -- means any member of the Board of Directors
of the Corporation who (i) is an outside director as defined under Section
162(m) of the Code and the regulations thereunder and (ii) a director who within
the prior year has not been, and is not being, granted any awards related to the
Shares under this Plan or any other plan of the Corporation or any of its
Affiliates except for awards which (A) are calculated in accordance with a
formula as contemplated in paragraph (c)(2)(ii) of Rule 16b-3 ("Rule 16b-3")
under the Securities Exchange Act of 1934; (B) result from participation in an
ongoing securities acquisition plan meeting the conditions of paragraph
(d)(2)(i) of Rule 16b-3; or, (C) arise from an election by a director to receive
all or part of his Board fees in securities.

                                       1
<PAGE>
 
          "Early Retirement" -- means retirement from employment with the
Corporation prior to the Participant either (i) having reached the age of 55 or
(ii) having maintained Continuous Service for at least three years.

          "Employee" -- means any person, including an officer, who is employed
by the Corporation or any Affiliate.

          "ERISA"  -- means the Employee Retirement Income Security Act of 1974,
as amended.

          "Exercise Price" -- means (i) in the case of an Option, the price per
Share at which the Shares subject to such Option may be purchased upon exercise
of such Option and (ii) in the case of a Right, the price per Share (other than
the Market Value per Share on the date of exercise and the Offer Price per Share
as defined in Section 10 hereof) which, upon grant, the Committee determines
shall be utilized in calculating the aggregate value which a Participant shall
be entitled to receive pursuant to Sections 9, 10 or 13 hereof upon exercise of
such Right.

          "Incentive Stock Option" -- means an option to purchase Shares granted
by the Committee pursuant to Section 6 hereof which is subject to the
limitations and restrictions of Section 8 hereof and is intended to qualify
under Section 422 of the Code.

          "Limited Stock Appreciation Right" -- means a stock appreciation right
with respect to Shares granted by the Committee pursuant to Sections 6 and 10
hereof.

          "Market Value" -- means the average of the high and low quoted sales
price on the date in question (or, if there is no reported sale on such date, on
the last preceding date on which any reported sale occurred) of a Share on the
Composite Tape for the New York Stock Exchange-Listed Stocks, or, if on such
date the Shares are not quoted on the Composite Tape, on the New York Stock
Exchange, or if the Shares are not listed or admitted to trading on such
Exchange, on the principal United States securities exchange registered under
the Securities Exchange Act of 1934 on which the Shares are listed or admitted
to trading, or, if the Shares are not listed or admitted to trading on any such
exchange, the mean between the closing high bid and low asked quotations with
respect to a Share on such date on the Nasdaq Stock Market, or any similar
system then in use, or, if no such quotations are available, the fair market
value on such date of a Share as the Committee shall determine.

          "Non-Qualified Stock Option" -- means an option to purchase Shares
granted by the Committee pursuant to Section 6 hereof, which option is not
intended to qualify under Section 422(b) of the Code.

          "Normal Retirement" -- means retirement from employment with the
Corporation after the Participant has (i) reached the age of 55 and (ii)
maintained Continuous Service for at least three years.

          "Option" -- means an Incentive Stock Option or a Non-Qualified Stock
Option.

                                       2
<PAGE>
 
          "Participant" -- means any officer or employee of the Corporation or
any Affiliate who is selected by the Committee to receive an Award.

          "Plan" -- means the 1995 Stock Option and Incentive Plan of the
Corporation.

          "Related" -- means (i) in the case of a Right, a Right which is
granted in connection with, and to the extent exercisable, in whole or in part,
in lieu of, an Option or another Right and (ii) in the case of an Option, an
Option with respect to which and to the extent a Right is exercisable, in whole
or in part, in lieu thereof has been granted.

          "Reload Option" -- means an Option to purchase Shares that is granted
pursuant to Section 6 hereof and is subject to the limitations and restrictions
of Section 7(g) hereof.

          "Restricted Period" -- means the period of time selected by the
Committee for the purpose of determining when restrictions are in effect under
Section 11 hereof with respect to Restricted Stock awarded under the Plan.

          "Restricted Stock" -- means Shares which have been contingently
awarded to a Participant by the Committee subject to the restrictions referred
to in Section 11 hereof, so long as such restrictions are in effect.

          "Right" -- means a Limited Stock Appreciation Right or a Stock
Appreciation Right.

          "Senior Officer" -- means the Corporation's president, principal
financial officer, or principal accounting officer, any vice president of the
Corporation in charge of a principal business unit, division or function (such
as sales, administration or finance), any other officer who performs a policy-
making function, or any other person who performs similar policy-making
functions for the Corporation.  Officers of the Corporation's Affiliates shall
be deemed Senior Officers of the Corporation if they perform such policy-making
functions for the Corporation.

          "Shares" -- means the shares of common stock of the Corporation.

          "Stock Appreciation Right" -- means a stock appreciation right with
respect to Shares granted by the Committee pursuant to Sections 6 and 9 hereof.

          "Ten Percent Beneficial Owner" -- means the beneficial owner of more
than ten percent of any class of the Corporation's equity securities registered
pursuant to Section 12 of the Securities Exchange Act of 1934.

      3.  Administration.  The Plan shall be administered by a Committee
          --------------                                                
consisting of two or more members, each of whom shall be a Disinterested Person.
The members of the Committee shall be appointed by the Board of Directors of the
Corporation.  Except as limited by the express provisions of the Plan, the
Committee shall have sole and complete authority and discretion to (i) select
Participants and grant Awards; (ii) determine the number of Shares to be subject
to types of Awards generally, as well as to individual Awards granted under the
Plan; 

                                       3
<PAGE>
 
(iii) determine the terms and conditions upon which Awards shall be granted
under the Plan; (iv) prescribe the form and terms of instruments evidencing such
grants; and (v) establish from time to time regulations for the administration
of the Plan, interpret the Plan, and make all determinations deemed necessary or
advisable for the administration of the Plan.

     A majority of the Committee shall constitute a quorum, and the acts of a
majority of the members present at any meeting at which a quorum is present, or
acts approved in writing by a majority of the Committee without a meeting, shall
be acts of the Committee.

     4.  Participation.  The Committee may select from time to time
         -------------                                             
Participants in the Plan from those officers and employees of the Corporation or
its Affiliates who, in the opinion of the Committee, have the capacity for
contributing to the successful performance of the Corporation or its Affiliates.

     5.  Shares Subject to Plan.  Subject to adjustment by the operation of
         ----------------------                                            
Section 12 hereof, the maximum number of shares with respect to which Awards may
be made under the Plan is 500,000 shares.  The Shares with respect to which
Awards may be made under the Plan may be either authorized and unissued shares
or issued shares heretofore or hereafter reacquired and held as treasury shares.
Shares which are subject to Related Rights and Related Options shall be counted
only once in determining whether the maximum number of Shares with respect to
which Awards may be granted under the Plan has been exceeded.  An Award shall
not be considered to have been made under the Plan with respect to any Option or
Right which terminates or with respect to Restricted Stock which is forfeited,
and new Awards may be granted under the Plan with respect to the number of
Shares as to which such termination or forfeiture has occurred.

     6.  General Terms and Conditions of Options and Rights.  The Committee
         --------------------------------------------------                
shall have full and complete authority and discretion, except as expressly
limited by the Plan, to grant Options and/or Rights and to provide the terms and
conditions (which need not be identical among Participants) thereof.  In
particular, the Committee shall prescribe the following terms and conditions:
(i) the Exercise Price of any Option or Right, which shall not be less than the
Market Value per Share at the date of grant of such Option or Right, (ii) the
number of Shares subject to, and the expiration date of, any Option or Right,
which expiration date shall not exceed ten years from the date of grant, (iii)
the manner, time and rate (cumulative or otherwise) of exercise of such Option
or Right, and (iv) the restrictions, if any, to be placed upon such Option or
Right or upon Shares which may be issued upon exercise of such Option or Right.
The Committee may, as a condition of granting any Option or Right, require that
a Participant agree not to thereafter exercise one or more Options or Rights
previously granted to such Participant.  Notwithstanding the foregoing, no
individual shall be granted awards in any calendar year with respect to more
than 25% of the total shares subject to the Plan.

                                       4
<PAGE>
 
      7.  Exercise of Options or Rights.
          ----------------------------- 

          (a) An Option or Right granted under the Plan shall be exercisable
during the lifetime of the Participant to whom such Option or Right was granted
only by such Participant, and except as provided in paragraphs (c), (d), (e) and
(f) of this Section 7, no such Option or Right may be exercised unless at the
time such Participant exercises such Option or Right, such Participant has
maintained Continuous Service since the date of grant of such Option or Right.
Cash settlements of Rights may be made only in accordance with any applicable
restrictions pursuant to Rule 16b-3(e) under the Securities Exchange Act of 1934
or any similar or successor provision.

          (b) To exercise an Option or Right under the Plan, the Participant to
whom such Option or Right was granted shall give written notice to the
Corporation in form satisfactory to the Committee (and, if partial exercises
have been permitted by the Committee, by specifying the number of Shares with
respect to which such Participant elects to exercise such Option or Right)
together with full payment of the Exercise Price, if any and to the extent
required.  The date of exercise shall be the date on which such notice is
received by the Corporation.  Payment, if any is required, shall be made either
(i) in cash (including check, bank draft or money order) or (ii) in the case of
an Option with respect to which Reload Options are authorized pursuant to
Section 7(f) hereof (or, in the case of any other Option, if permitted by the
Committee), by delivering (A) Shares already owned by the Participant and having
a fair market value equal to the applicable exercise price, such fair market
value to be determined in such appropriate manner as may be provided by the
Committee or as may be required in order to comply with or to conform to
requirements of any applicable laws or regulations, or (B) a combination of cash
and such Shares.

          (c) If a Participant to whom an Option or Right was granted shall
cease to maintain Continuous Service for any reason (including total and partial
disability and Early Retirement, but excluding Normal Retirement, death and
termination of employment by the Corporation or any Affiliate for cause), such
Participant may, but only within the period of three months immediately
succeeding such cessation of Continuous Service and in no event after the
expiration date of such Option or Right, exercise such Option or Right to the
extent that such Participant was entitled to exercise such Option or Right at
the date of such cessation, provided, however, that such right of exercise after
cessation of Continuous Service shall not be available to a Participant if the
Committee otherwise determines and so provides in the applicable instrument or
instruments evidencing the grant of such Option or Right.  If the Continuous
Service of a Participant to whom an Option or Right was granted by the
Corporation is terminated for cause, all rights under any Option or Right of
such Participant shall expire immediately upon the giving to the Participant of
notice of such termination.

          (d) If a Participant to whom an Option or Right was granted shall
cease to maintain Continuous Service due to Normal Retirement, such Participant
may, but only within the period of two years immediately succeeding such
cessation of Continuous Service and in no event after the expiration date of
such Option or Right, exercise such Option or Right to the extent that such
Participant was entitled to exercise such Option or Right at the date of such
cessation, provided, however, that such right of exercise after cessation of
Continuous Service 

                                       5
<PAGE>
 
shall not be available to a Participant if the Committee otherwise determines
and so provides in the applicable instrument or instruments evidencing the grant
of such Option or Right.

          (e) In the event of the death of a Participant while in the Continuous
Service of the Corporation or an Affiliate or within the three month or two year
periods referred to in paragraphs (c) and (d), respectively, of this Section 7,
the person to whom any Option or Right held by the Participant at the time of
his death is transferred by will or the laws of descent and distribution or in
the case of an Award other than an Incentive Stock Option, pursuant to a
qualified domestic relations order, as defined in the Code or Title I of ERISA
or the rules thereunder may, but only to the extent such Participant was
entitled to exercise such Option or Right immediately prior to his death,
exercise such Option or Right at any time within a period of two years
succeeding the date of death of such Participant, but in no event later than ten
years from the date of grant of such Option or Right.  Following the death of
any Participant to whom an Option was granted under the Plan, irrespective of
whether any Related Right shall have theretofore been granted to the Participant
or whether the person entitled to exercise such Related Right desires to do so,
the Committee may, as an alternative means of settlement of such Option, elect
to pay to the person to whom such Option is transferred by will or by the laws
of descent and distribution or in the case of an Option other than an Incentive
Stock Option, pursuant to a qualified domestic relations order, as defined in
the Code or Title I of ERISA or the rules thereunder, the amount by which the
Market Value per Share on the date of exercise of such Option shall exceed the
Exercise Price of such Option, multiplied by the number of shares with respect
to which such Option is properly exercised.  Any such settlement of an Option
shall be considered an exercise of such Option for all purposes of the Plan.

     (f) Notwithstanding the provisions of subparagraphs (c) through (e) above,
the Committee may, in its sole discretion, establish different terms and
conditions pertaining to the effect of termination to the extent permitted by
applicable federal and state law.

     (g) Concurrently with the grant of any Option (an "Underlying Option"), the
Committee may authorize Reload Options permitting the grantee of the Underlying
Option to purchase for cash, Shares or a combination thereof an aggregate number
of Shares not greater than the sum of (i) the number of Mature Shares (as
defined hereinbelow) used in exercises of the Underlying Option and (ii) to the
extent authorized by the Committee, the number of Mature Shares used to satisfy
any tax withholding requirement incident to exercises of the Underlying Option.
The grant of each Reload Option so authorized by the Committee shall become
effective upon the exercise (a "Stock Exercise") of all or part of the
Underlying Option through the use of Shares held by the optionee for at least 12
months prior to such exercise ("Mature Shares"), provided, however, that no
Reload Option shall first become effective after the optionee has ceased to
maintain Continuous Service. Reload Options may be authorized with respect to
Options that are themselves granted as Reload Options. Upon each Stock Exercise
of an Underlying Option, the Exercise Price of the resulting Reload Option, the
number of Shares covered thereby, and, in the discretion of the Committee and
subject to the limitations and restrictions of Section 8 hereof, the
determination that the Reload Option is intended to qualify as an Incentive
Stock Option, shall be evidenced through an amendment to the agreement or other
instrument evidencing the Underlying Option. The Exercise Price of a Reload
Option shall be the Market Value per Share on the date the grant of the Reload
Option becomes effective.

                                       6
<PAGE>
 
Each Reload Option shall become fully exercisable six months from its effective
date. The term of each Reload Option shall be equal to the remaining term of the
Underlying Option.

      8.  Incentive Stock Options.  Any provision of the Plan to the contrary
          -----------------------                                            
notwithstanding, (i) no Incentive Stock Option shall be granted more than ten
years from the date the Plan is adopted by the Board of Directors of the
Corporation and no Incentive Stock Option shall be exercisable more than ten
years from the date such Incentive Stock Option is granted, (ii) the Exercise
Price of any Incentive Stock Option shall not be less than the Market Value per
Share on the date such Incentive Stock Option is granted, (iii) any Incentive
Stock Option shall not be transferable by the Participant to whom such Incentive
Stock Option is granted other than by will or the laws of descent and
distribution and shall be exercisable during such Participant's lifetime only by
such Participant, (iv) no Incentive Stock Option shall be granted to any
individual who, at the time such Incentive Stock Option is granted, owns stock
possessing more than 10% of the total combined voting power of all classes of
stock of the Corporation or any Affiliate unless the Exercise Price of such
Incentive Stock Option is at least 110% of the Market Value per Share at the
date of grant and such Incentive Stock Option is not exercisable after the
expiration of five years from the date such Incentive Stock Option is granted,
and (v) the aggregate Market Value (determined as of the time any Incentive
Stock Option is granted) of the Shares with respect to which Incentive Stock
Options are exercisable for the first time by a Participant in any calendar year
shall not exceed $100,000.

      9.  Stock Appreciation Rights.  A Stock Appreciation Right shall, upon its
          -------------------------                                             
exercise, entitle the Participant to whom such Stock Appreciation Right was
granted to receive a number of Shares or cash or combination thereof, as the
Committee in its discretion shall determine, the aggregate value of which (i.e.,
the sum of the amount of cash and/or Market Value of such Shares on date of
exercise) shall equal (as nearly as possible, it being understood that the
Corporation shall not issue any fractional shares) the amount by which the
Market Value per Share on the date of such exercise shall exceed the Exercise
Price of such Stock Appreciation Right, multiplied by the number of Shares with
respect of which such Stock Appreciation Right shall have been exercised.  A
Stock Appreciation Right may be Related to an Option or may be granted
independently of any Option as the Committee shall from time to time in each
case determine.  At the time of grant of an Option the Committee shall determine
whether and to what extent a Related Stock Appreciation Right shall be granted
with respect thereto; provided, however, and notwithstanding any other provision
of the Plan, that if the Related Option is an Incentive Stock Option, the
Related Stock Appreciation Right shall satisfy all the restrictions and
limitations of Section 8 hereof as if such Related Stock Appreciation Right were
an Incentive Stock Option and as if other rights which are Related to Incentive
Stock Options were Incentive Stock Options.  In the case of a Related Option,
such Related Option shall cease to be exercisable to the extent of the Shares
with respect to which the Related Stock Appreciation Right was exercised.  Upon
the exercise or termination of a Related Option, any Related Stock Appreciation
Right shall terminate to the extent of the Shares with respect to which the
Related Option was exercised or terminated.  Notwithstanding the foregoing, no
Stock Appreciation Right shall be exercisable by a director, Senior Officer or
Ten Percent Beneficial Owner of the Corporation within six months of the date of
its grant.

     10.  Limited Stock Appreciation Rights.  At the time of grant of an Option
          ---------------------------------                                    
or Stock Appreciation Right to any Participant, the Committee shall have full
and complete authority and 

                                       7
<PAGE>
 
discretion to also grant to such Participant a Limited Stock Appreciation Right
which is related to such Option or Stock Appreciation Right; provided, however
and notwithstanding any other provision of the Plan, that if the Related Option
is an Incentive Stock Option, the Related Limited Stock Appreciation Right shall
satisfy all the restrictions and limitations of Section 8 hereof as if such
Related Limited Stock Appreciation Right were an Incentive Stock Option and as
if all other Rights which are Related to Incentive Stock Options were Incentive
Stock Options. Notwithstanding any other provision of the Plan, a Limited Stock
Appreciation Right shall be exercisable only during the period beginning on the
first day following the date of expiration of any "offer" (as such term is
hereinafter defined) and ending on the forty-fifth day following such date,
provided, however, that no Limited Stock Appreciation Right shall be exercisable
by a director or officer of the Corporation within six months of the date of its
grant.

     A Limited Stock Appreciation Right shall, upon its exercise, entitle the
Participant to whom such Limited Stock Appreciation Right was granted to receive
an amount of cash equal to the amount by which the "Offer Price per Share" (as
such term is hereinafter defined) or the Market Value on the date of such
exercise, as shall have been provided by the Committee in its discretion at the
time of grant, shall exceed the Exercise Price of such Limited Stock
Appreciation Right, multiplied by the number of Shares with respect to which
such Limited Stock Appreciation Right shall have been exercised.  Upon the
exercise of a Limited Stock Appreciation Right, any Related Option and/or
Related Stock Appreciation Right shall cease to be exercisable to the extent of
the Shares with respect to which such Limited Stock Appreciation Right was
exercised.  Upon the exercise or termination of a Related Option or Related
Stock Appreciation Right, any Related Limited Stock Appreciation Right shall
terminate to the extent of the Shares with respect to which such Related Option
or Related Stock Appreciation Right was exercised or terminated.

     For the purposes of this Section 10, the term "Offer" shall mean any tender
offer or exchange offer for Shares other than one made by the Corporation,
provided that the corporation, person or other entity making the offer acquires
pursuant to such offer either (i) 25% of the Shares outstanding immediately
prior to the commencement of such offer or (ii) a number of shares which,
together with all other shares acquired in any tender offer or exchange offer
(other than one made by the Corporation) which expired within sixty days of the
expiration date of the offer in question, equals 25% of the Shares outstanding
immediately prior to the commencement of the offer in question.  The term "Offer
Price per Share" as used in this Section 10 shall mean the highest price per
Share paid in any Offer which Offer is in effect any time during the period
beginning on the sixtieth day prior to the date on which a Limited Stock
Appreciation Right is exercised and ending on the date on which such Limited
Stock Appreciation Right is exercised.  Any securities or property which are
part or all of the consideration paid for Shares in the Offer shall be valued in
determining the Offer Price per Share at the higher of (i) the valuation placed
on such securities or property by the corporation, person or other entity making
such Offer or (ii) the valuation placed on such securities or property by the
Committee.

     11.  Terms and Conditions of Restricted Stock.  The Committee shall have
          ----------------------------------------                           
full and complete authority, subject to the limitations of the Plan, to grant
awards of Restricted Stock and, in addition to the terms and conditions
contained in paragraphs (a) through (f) of this Section 11, to provide such
other terms and conditions (which need not be identical among 

                                       8
<PAGE>
 
Participants) in respect of such Awards, and the vesting thereof, as the
Committee shall determine and provide in the agreement referred to in paragraph
(d) of this Section 11.

          (a) At the time of an award of Restricted Stock, the Committee shall
establish for each Participant a Restricted Period during which or at the
expiration of which, as the Committee shall determine and provide in the
agreement referred to in paragraph (d) of this Section 11, the shares awarded as
Restricted Stock shall vest, and subject to any such other terms and conditions
as the Committee shall provide shares of Restricted Stock may not be sold,
assigned, transferred, pledged or otherwise encumbered by the Participant,
except as hereinafter provided, during the Restricted Period.  Except for such
restrictions, and subject to paragraphs (c), (d) and (e) of this Section 11 and
Section 12 hereof, the Participant as owner of such shares shall have all the
rights of a stockholder including but not limited to the right to receive all
dividends paid on such shares and the right to vote such shares.  The Committee
shall have the authority, in its discretion, to accelerate the time at which any
or all of the restrictions shall lapse with respect to any shares of Restricted
Stock prior to the expiration of the Restricted Period with respect thereto, or
to remove any or all of such restrictions, whenever it may determine that such
action is appropriate by reason of changes in applicable tax or other laws or
other changes in circumstances occurring after the commencement of such
Restricted Period.

          (b) Except as provided in Section 14 hereof, if a Participant ceases
to maintain Continuous Service for any reason (other than death, total or
partial disability or Normal or Early Retirement) unless the Committee shall
otherwise determine and provide in the agreement referred to in paragraph (d) of
this Section 11, all shares of Restricted Stock theretofore awarded to such
Participant and which at the time of such termination of Continuous Service are
subject to the restrictions imposed by paragraph (a) of this Section 11 shall
upon such termination of Continuous Service be forfeited and returned to the
Corporation.  Unless the Committee shall have provided in the agreement referred
to in paragraph (d) of this Section 11 for a ratable lapse of restrictions with
respect to an award of shares of Restricted Stock during the Restricted Period,
if a Participant ceases to maintain Continuous Service by reason of death, total
or partial disability or Normal or Early Retirement, such portion of such shares
of Restricted Stock awarded to such Participant which at the time of such
termination of Continuous Service are subject to the restrictions imposed by
paragraph (a) of this Section 11 as shall be equal to the portion of the
Restricted Period with respect to such shares which shall have elapsed at the
time of such termination of Continuous Service shall be free of restrictions and
shall not be forfeited.

          (c) Each certificate in respect of shares of Restricted Stock awarded
under the Plan shall be registered in the name of the Participant and deposited
by the Participant, together with a stock power endorsed in blank, with the
Corporation and shall bear the following (or a similar) legend:

          "The transferability of this certificate and the shares of stock
     represented hereby are subject to the terms and conditions (including
     forfeiture) contained in the 1995 Stock Option and Incentive Plan of Bay
     View Capital Corporation and an Agreement entered into between the
     registered owner and Bay View Capital Corporation.  Copies of such Plan and
     Agreement are on file in the offices of the Secretary of Bay View Capital
     Corporation, 2121 South El Camino Real, San Mateo, California 94403."

                                       9
<PAGE>
 
          (d) At the time of an award of shares of Restricted Stock, the
Participant shall enter into an Agreement with the Corporation in a form
specified by the Committee, agreeing to the terms and conditions of the award
and such other matters as the Committee shall in its sole discretion determine.

          (e) At the time of an award of shares of Restricted Stock, the
Committee may, in its discretion, determine that the payment to the Participant
of dividends declared or paid on such shares, or a specified portion thereof, by
the Corporation shall be deferred until the earlier to occur of (i) the lapsing
of the restrictions imposed under paragraph (a) of this Section 11 or (ii) the
forfeiture of such shares under paragraph (b) of this Section 11, and shall be
held by the Corporation for the account of the Participant until such time.  In
the event of such deferral, there shall be credited at the end of each year (or
portion thereof) interest on the amount of the account at the beginning of the
year at a rate per annum as the Committee, in its discretion, may determine.
Payment of deferred dividends, together with interest accrued thereon as
aforesaid, shall be made upon the earlier to occur of the events specified in
(i) and (ii) of the immediately preceding sentence.

          (f) At the expiration of the restrictions imposed by paragraph (a) of
this Section 11, the Corporation shall redeliver to the Participant (or where
the relevant provision of paragraph (b) of this Section 11 applies in the case
of a deceased Participant, to his legal representative, beneficiary or heir) the
certificate(s) and stock power deposited with it pursuant to paragraph (c) of
this Section 11 and the Shares represented by such certificate(s) shall be free
of the restrictions referred to in paragraph (a) of this Section 11.

     12.  Adjustments Upon Changes in Capitalization.  In the event of any
          ------------------------------------------                      
change in the outstanding Shares subsequent to the effective date of the Plan by
reason of any reorganization, recapitalization, stock split, stock dividend,
combination or exchange of shares, merger, consolidation or any change in the
corporate structure or Shares of the Corporation, the maximum aggregate number
and class of shares as to which Awards may be granted under the Plan and the
number and class of shares with respect to which Awards theretofore have been
granted under the Plan and shall be appropriately adjusted by the Committee,
whose determination shall be conclusive.  Any shares of stock or other
securities received, as a result of any of the foregoing, by a Participant with
respect to Restricted Stock shall be subject to the same restrictions and the
certificate(s) or other instruments representing or evidencing such shares or
securities shall be legended and deposited with the Corporation in the manner
provided in Section 11 hereof.

     13.  Effect of Merger on Options or Rights.  In the case of any merger,
          -------------------------------------                             
consolidation or combination of the Corporation (other than a merger,
consolidation or combination in which the Corporation is the continuing
corporation and which does not result in the outstanding Shares being converted
into or exchanged for different securities, cash or other property, or any
combination thereof), any Participant to whom an Option or Right has been
granted at least six months prior to such event shall have, in addition to the
rights of exercise pursuant to Section 7 hereof, the right (subject to the
provisions of the Plan and any limitation applicable to such Option or Right),
thereafter and during the term of each such Option or Right, to receive upon
exercise of any such Option or Right an amount equal to the excess of the fair
market value on the date of such exercise of the securities, cash or other
property, or combination thereof, 

                                       10
<PAGE>
 
receivable upon such merger, consolidation or combination in respect of a Share
over the Exercise Price of such Right or Option, multiplied by the number of
Shares with respect to which such Option or Right shall have been exercised.
Such amount may be payable fully in cash, fully in one or more of the kind or
kinds of property payable in such merger, consolidation or combination, or
partly in cash and partly in one or more of such kind or kinds of property, all
in the discretion of the Committee.

     14.  Effect of Change in Control.  Each of the events specified in the
          ---------------------------                                      
following clauses (i) through (iii) of this Section 14 shall be deemed a "change
of control":  (i) any third person, including a "group" as defined in Section
13(d)(3) of the Securities Exchange Act of 1934, shall become the beneficial
owner of shares of the Corporation with respect to which 25% or more of the
total number of votes for the election of the Board of Directors of the
Corporation may be cast, (ii) as a result of, or in connection with, any cash
tender offer, merger or other business combination, sale of assets or contested
election, or combination of the foregoing, the persons who were directors of the
Corporation shall cease to constitute a majority of the Board of Directors of
the Corporation, or (iii) the stockholders of the Corporation shall approve an
agreement providing either for a transaction in which the Corporation will cease
to be an independent publicly-owned corporation or for a sale or other
disposition of all or substantially all the assets of the Corporation.  Upon a
change in control, unless the Committee shall have otherwise provided in the
agreement referred to in paragraph (d) of Section 11 hereof, any Restricted
Period with respect to Restricted Stock theretofore awarded to such Participant
shall lapse upon such termination and all Shares awarded as Restricted Stock
shall become fully vested in the Participant to whom such Shares were awarded.
If a tender offer or exchange offer for Shares (other than such an offer by the
Corporation) is commenced, or if the event specified in clause (iii) above shall
occur, unless the Committee shall have otherwise provided in the instrument
evidencing the grant of an Option or Stock Appreciation Right, all Options and
Stock Appreciation Rights theretofore granted and not fully exercisable shall
become exercisable in full upon the happening of such event; provided, however,
that no Option or Stock Appreciation Right shall be exercisable by a director or
officer of the Corporation within six months of the date of grant of such Option
or Stock Appreciation Right and no Option or Stock Appreciation Right which has
previously been exercised or otherwise terminated shall become exercisable.

     15.  Assignments and Transfers.  No Award nor any right or interest of a
          -------------------------                                          
Participant under the Plan in any instrument evidencing any Award under the Plan
may be assigned, encumbered or transferred except, in the event of the death of
a Participant, by will or the laws of descent and distribution, or in the case
of Awards other than Incentive Stock Options pursuant to a qualified domestic
relations order, as defined in the Code or Title I of ERISA or the rules
thereunder.

     16.  Employee Rights Under the Plan.  No officer or employee shall have a
          ------------------------------                                      
right to be selected as a Participant nor, having been so selected, to be
selected again as a Participant and no officer, employee or other person shall
have any claim or right to be granted an Award under the Plan or under any other
incentive or similar plan of the Corporation or any Affiliate. Neither the Plan
nor any action taken thereunder shall be construed as giving any employee any
right to be retained in the employ of the Corporation or any Affiliate.

                                       11
<PAGE>
 
     17.  Delivery and Registration of Stock.  The Corporation's obligation to
          ----------------------------------                                  
deliver Shares with respect to an Award shall, if the Committee so requests, be
conditioned upon the receipt of a representation as to the investment intention
of the Participant to whom such Shares are to be delivered, in such form as the
Committee shall determine to be necessary or advisable to comply with the
provision of the Securities Act of 1933 or any other federal, state or local
securities legislation.  It may be provided that any representation requirement
shall become inoperative upon a registration of the Shares or other action
eliminating the necessity of such representation under such Securities Act or
other securities legislation.  The Corporation shall not be required to deliver
any Shares under the Plan prior to (i) the admission of such shares to listing
on any stock exchange on which Shares may then be listed, and (ii) the
completion of such registration or other qualification of such Shares under any
state or federal law, rule or regulation, as the committee shall determine to be
necessary or advisable.

     This Plan is intended to comply with Rule 16b-3 under the Securities
Exchange Act of 1934.  Any provision of the Plan which is inconsistent with said
Rule shall, to the extent of such inconsistency, be inoperative and shall not
affect the validity of the remaining provisions of the Plan.

     18.  Withholding Tax.  Upon the termination of the Restricted Period with
          ---------------                                                     
respect to any shares of Restricted Stock (or at any such earlier time, if any,
that an election is made by the Participant under Section 83(b) of the Code, or
any successor provision thereto, to include the value of such shares in taxable
income), the Corporation shall have the right to require the Participant or
other person receiving such shares to pay the Corporation the amount of any
taxes which the Corporation is required to withhold with respect to such shares,
or, in lieu thereof, to retain or sell without notice, a sufficient number of
shares held by it to cover the amount required to be withheld.  The Corporation
shall have the right to deduct from all dividends paid with respect to shares of
Restricted Stock the amount of any taxes which the Corporation is required to
withhold with respect to such dividend payments.

     The Corporation shall have the right to deduct from all amounts paid in
cash with respect to the exercise of a Right under the Plan any taxes required
by law to be withheld with respect to such cash payments.  Where a Participant
or other person is entitled to receive Shares pursuant to the exercise of an
Option or Right pursuant to the Plan, the Corporation shall have the right to
require the Participant or such other person to pay the Corporation the amount
of any taxes which the Corporation is required to withhold with respect to such
Shares, or, in lieu thereof, to retain, or sell without notice, a number of such
shares sufficient to cover the amount required to be withheld.

     19.  Amendment or Termination.  The Board of Directors of the Corporation
          ------------------------                                            
may amend, suspend or terminate the Plan or any portion thereof at any time, but
(except as provided in Section 12 hereof) no amendment shall be made without
approval of the stockholders of the Corporation which shall (i) materially
increase the benefits accruing to participants under the Plan; (ii) materially
increase the number of securities which may be issued under the Plan; or (iii)
materially modify the requirements as to eligibility for participation in the
Plan, provided, however, that no such amendment, suspension or termination shall
impair the rights of any Participant, without his consent, in any Award
theretofore made pursuant to the Plan.

                                       12
<PAGE>
 
     20.  Effective Date and Term of Plan.  The Plan shall become effective upon
          -------------------------------                                       
its adoption by the Board of Directors of the Corporation, subject to the
approval of the Plan by the shareholders of the Corporation.  It shall continue
in effect for a term of ten years unless sooner terminated under Section 19
hereof.

                                       13