<PAGE>
 
                                                                   Exhibit 10.27
 
                        THE CARBIDE/GRAPHITE GROUP, INC.

                  NON EMPLOYEE DIRECTOR STOCK-BASED INCENTIVE
                               COMPENSATION PLAN



     1.  Purpose of the Plan
         -------------------

          The purpose of the Plan is to assist the Company, and its Subsidiaries
and Affiliates, in attracting and retaining valued members of the Board of
Directors of the Company by offering them a greater stake in the Company's
success and a closer identity with it, and to encourage ownership of the
Company's stock by such directors.

     2.  Definitions
         -----------

          2.1.  "Affiliate" means any entity other than a Subsidiary in which
the Company has a substantial direct or indirect equity interest, as determined
by the Board.

          2.2. "Award" means an award of Options under the Plan pursuant to the
award formulas provided for herein.

          2.3. "Board" means the Board of Directors of the Company.

          2.4.  "Change in Control" means a change in control of the Company of
a nature that would be required to be reported in response to Item 6(e) of
Schedule 14A of Regulation 14A promulgated under the 1934 Act, whether or not
the Company is then subject to such reporting requirement; provided that,
without limitation, a Change in Control shall be deemed to have occurred if (i)
any individual, partnership, firm, corporation, association, trust,
unincorporated organization or other entity, or any syndicate or group deemed to
be a person under Section 14(d)(2) of the 1934 Act, is or becomes the
"beneficial owner" (as defined in Rule 13d-3 of the General Rules and
Regulations under the 1934 Act), directly or indirectly, of securities of the
Company representing 20% or more of the combined voting power of the Company's
then outstanding securities entitled to vote in the election of directors of the
Company; or (ii) during any period of two consecutive years (not including any
period prior to the execution of this Plan), individuals who at the beginning of
such period constitute the Board and any new directors, whose election by the
Board or nomination for election by the Company's stockholders was approved by a
vote of a majority of the directors then still in office who either were
directors at the beginning of the period or whose election or nomination for
election was previously so approved, cease for any reason to constitute a
majority thereof.

          2.5. "Code" means the Internal Revenue Code of 1986, as amended.
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          2.6.  "Common Stock" means the common stock of the Company, par value
$.01 a share, or such other class or kind of shares or other securities
resulting from the application of Section 6.

          2.7. "Company" means The Carbide/Graphite Group, Inc., a Delaware
corporation, or any successor corporation.

          2.8.  "Committee" means the committee designated by the Board to
administer the Plan under Section 4 or, in the absence of such designation, the
Board of Directors.

          2.9.  "Disability" means termination of membership on the Board of
Directors of the Company as a result of a Non Employee Director's inability to
perform substantially his or her duties and responsibilities as a director by
reason of a physical or mental disability or infirmity (i) for a continuous
period of six months or (ii) at such earlier time as such Employee submits
medical evidence satisfactory to the Committee that such Employee has a physical
or mental disability or infirmity that will likely prevent such Employee from
substantially performing his or her duties and responsibilities for six months
or longer. The date of such Disability shall be the earlier of the last day of
such six-month period or the day on which such Employee submits such evidence.

          2.10.  "Non Employee Director" means a member of the Board of
Directors of the Company who is not an officer or employee of the Company, but
the furnishing of consulting services or advisory services for compensation to
the Company, a Subsidiary or an Affiliate, shall not be construed to constitute
a director as an employee.

          2.11.  "Fair Market Value" means, on any given date, (i) the mean
between the highest and lowest prices of actual sales of shares of Common Stock
on the principal national securities exchange on which the Common Stock is
listed on such date or, if Common Stock was not traded on such date, on the next
preceding day on which the Common Stock was traded or (ii) if the Common Stock
is listed on the National Association of Securities Dealers Automated Quotation
System ("NASDAQ"), the mean between the bid and asked price at the close of
business on such day.

          2.12. "Holder" means a Non Employee Director to whom an Award is made.

          2.13. "1934 Act" means the Securities Exchange Act of 1934, as
amended.

          2.14.  "Non Qualified Option" means a stock option not intended to be
an incentive stock option within the meaning of Code (S) 422, and designated as
a Non Qualified Option.

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          2.15. "Option" means any stock option granted from time to time under
the Plan.

          2.16.  "Plan" means The Carbide/Graphite Group, Inc. Non Employee
Director Stock-Based Incentive Compensation Plan herein set forth, as amended
from time to time.

          2.17.  "Subsidiary" means any corporation (other than the Company) in
an unbroken chain of corporations beginning with the Company (or any subsequent
parent of the Company) if each of the corporations other than the last
corporation in the unbroken chain owns stock possessing 50% or more of the total
combined voting power of all classes of stock in one of the other corporations
in such chain.

     3.  Eligibility
         ------------

          All Non Employee Directors are automatically eligible to receive
Awards.

    4.  Administration of Plan
        ----------------------

          It is intended that all Awards pursuant to this Plan be formula awards
within the meaning of Rule 16b-3(c)(2)(ii) under Section 16 of the Exchange Act,
and the Plan shall be applied and operated to effect that intent. To the extent
that recordkeeping and other ministerial functions must be performed to
administer and operate the Plan properly, either the Board or a committee
appointed by the Board consisting of not fewer than two individuals shall
perform such administrative functions. The Board shall have the discretion to
remove and appoint members of the committee from time to time.

     5.  Grants of Awards Under the Plan
         -------------------------------

          5.1.  Grant of Awards.  Each Non Employee Director who is a member of
                ---------------                                                
the Board of Directors on August 26, 1996 shall be granted:  (x) an option to
purchase 1,700 Shares at the Fair Market Value of the Common Stock on August 26,
1996; provided that such option may not be exercised and shall not vest unless
such Non Employee Director is a member of the Board on July 31, 1997; (y) so
long as he is a Non Employee Director on July 31, 1997, an option to purchase
1,700 Shares at the Fair Market Value of the Common Stock on July 31, 1997;
provided that such option may not be exercised and shall not vest unless such
Non Employee Director is a member of the Board on July 31, 1998; and (z) so long
as he is a Non Employee Director on July 31, 1998, an option to purchase 1,700
Shares at the Fair Market Value of the Common Stock on July 31, 1998; provided
that such option may not be exercised and shall not vest unless such Non
Employee Director is a member of the Board on July 31, 1999.  Each Non Employee
Director who is elected or appointed to the Board for the first time subsequent
to August 26, 1996, shall be granted:  (x) an option to purchase 1,700 Shares

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at the Fair Market Value of the Common Stock on the date such additional Non
Employee Director becomes a member of the Board; provided that such option may
not be exercised and shall not vest unless such Non Employee Director is a
member of the Board on the July 31st next following the date of grant (the
"First Vesting Date"); (y) so long as he is then a Non Employee Director, an
option to purchase 1,700 Shares at the Fair Market Value of the Common Stock on
the First Vesting Date; provided that such option may not be exercised and shall
not vest unless such Non Employee Director is a member of the Board on the first
anniversary of the First Vesting Date; and (z) so long as he is then a Non
Employee Director, an option to purchase 1,700 Shares at the Fair Market Value
of the Common Stock on the first anniversary of the First Vesting Date; provided
that such option may not be exercised and shall not vest unless such Non
Employee Director is a member of the Board on the second anniversary of the
First Vesting Date.  Options granted hereunder shall have a term of ten years
from the date of grant.

          5.2.  No Reduction in Shares.  Any shares issued by the Company
                ----------------------                                   
through the assumption or substitution of outstanding grants from an acquired
company shall not reduce the shares available for Awards under the Plan. Any
shares issued hereunder may consist, in whole or in part, of authorized and
unissued shares or treasury shares. If any shares subject to any Award granted
hereunder are forfeited or such Award otherwise terminates without the issuance
of such shares or the payment of other consideration in lieu of such shares, the
shares subject to such Award, to the extent of any such forfeiture or
termination, shall again be available for Awards under the Plan.

          5.3.  Restriction on Transferability.  No Option shall be transferable
                ------------------------------                                  
otherwise than by will or the laws of descent and distribution and, during the
lifetime of the Holder, shall be exercisable only by the Holder. Upon the death
of a Holder, the person to whom the rights have passed by will or by the laws of
descent and distribution may exercise an Option only in accordance with this
Section 5.

          5.4.  Payment of Option Price.  The Option price of the shares of
                -----------------------                                    
Common Stock upon the exercise of an Option shall be paid in full (i) in cash at
the time of exercise, (ii) in whole or in part in shares of Common Stock valued
at Fair Market Value or (iii) in whole or in part by the delivery of additional,
unexercised Non Qualified Stock Options (based on the difference between the
Fair Market Value of the Common Stock for which they are exercisable and the
exercise price of such additional Non Qualified Stock Options).

          5.5.  Termination by Death.  If a Non Employee Director's service as a
                --------------------                                            
director of the Company terminates by reason of death, any Option held by such
Non Employee Director may thereafter be exercised to the extent such Option was
exercisable at the time of death by the legal representative of the Holder or by
any person to whom the rights have passed by will or by the laws of descent and
distribution, for a period of

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one year from the date of such death or until the expiration of the stated term
of such Option, whichever period is shorter.

          5.6.  Termination by Reason of Disability.  If a Non Employee
                -----------------------------------                    
Director's service as a director of the Company terminates by reason of
Disability, any Option held by such Non Employee Director may thereafter be
exercised by the Non Employee Director (or, where appropriate, the Non Employee
Director's legal representative) to the extent it was exercisable at the time of
termination for a period of 18 months from the date of such termination of
employment or until the expiration of the stated term of such Option, whichever
period is shorter; provided, however, that if the Non Employee Director dies
within such 18 month period, any unexercised Option held by such Non Employee
Director shall thereafter be exercisable to the extent to which it was
exercisable at the time of death for a period of 12 months from the date of such
death or until the expiration of the stated term of such Option, whichever
period is shorter.

          5.7.  Other Termination.  If a Non Employee Director's service as a
                -----------------                                            
director of the Company terminates for any reason other than death or
Disability, the Option shall be exercisable, to the extent otherwise then
exercisable, for the lesser of three months from the date of such termination or
the balance of such Option's term, after which such Option will terminate.


    6.  Adjustments Upon Changes in Capitalization
        ------------------------------------------

          In the event of a reorganization, recapitalization, stock split, spin-
off, splitoff, split up, stock dividend, combination of shares, merger,
consolidation or any other change in the corporate structure of the Company
affecting Common Stock, or a sale by the Company of all or part of its assets,
or any distribution to stockholders other than a cash dividend, the Board shall
make appropriate adjustment in the number and kind of shares authorized by the
Plan and any adjustments to outstanding Awards as it determines appropriate. No
fractional shares of Common Stock shall be issued pursuant to such an
adjustment. The Fair Market Value of any fractional shares resulting from
adjustments pursuant to this Section shall, where appropriate, be paid in cash
to the Holder.

    7.  Effective Date, Termination and Amendment
        -----------------------------------------

          The Plan shall become effective on August 26, 1996.  The Plan shall
remain in full force and effect until the earlier of August, 2006 or the date it
is terminated by the Board. The Board shall have the power to amend, suspend or
terminate the Plan at any time; provided, however, that this Plan shall not be
amended more than once in any 6 month period, other than to comport with changes
in the Code.

    8.  Execution and Delivery of Stockholders Agreement
        ------------------------------------------------

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          Unless otherwise determined by the Committee or the Board of
Directors, as the case may be, no shares of Common Stock shall be issued or
transferred pursuant to an Award unless and until the Holder, or any person to
whom rights have passed by will or by the laws of descent and distribution, has
executed and delivered to the Company or the Committee or the Board of
Directors, as the case may be, the Stockholders Agreement, dated May ___, 1995,
by and among the Company and the Management Stockholders named therein.

    9.  Non-Assignability
        -----------------

          Awards may not be pledged, assigned or transferred for any reason
during the Holder's lifetime, and any attempt to do so shall be void and the
relevant Award shall be forfeited.

    10.  General Provisions
         ------------------

          10.1.  No Right to Position.  Nothing contained in the Plan, or any
                 --------------------                                        
Award granted pursuant to the Plan, shall confer upon any Non Employee Director
any right with respect to continuance of service as a director of the Company.

          10.2.  Governing Law. To the extent that Federal laws (including, but
                 -------------                                                 
not limited to, the 1934 Act, the Code and the Employee Retirement Income
Security Act of 1974, as amended) do not otherwise control, the Plan and all
determinations made and actions taken pursuant hereto shall be governed by the
laws of the State of Delaware and construed accordingly.

          10.3.  Compliance with Law. No shares of Common Stock shall be issued
                 -------------------                                           
or transferred pursuant to an Award unless and until all applicable requirements
imposed by Federal and state securities and other laws, rules and regulations
and by any stock exchange upon which the Common Stock may be listed have been
met. The Company may require the Holder to take any reasonable action to meet
such requirements. The Plan is intended to conform to the requirements of a
"formula plan" pursuant to Section 16(b) of the Securities Act of 1934 and the
Rules and Regulations thereunder and any provisions of the Plan which are
inconsistent with such requirements are void and of no effect.

    11.  Change in Control
         -----------------

          Notwithstanding any other provision of the Plan to the contrary, upon
the occurrence of a Change in Control all outstanding Options shall become
immediately exercisable and shall remain exercisable for 30 days following the
involuntary termination of the Non Employee Director's service as a member of
the Board of Directors of the Company (other than for cause, which shall mean
misappropriation of funds, habitual insobriety, substance abuse, conviction of a
crime involving moral turpitude, willful and

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material misrepresentation to the directors of the employer or gross negligence
in the performance of duties having a material adverse effect on the business,
operations, assets, properties or financial condition of the employer) within 18
months following such Change in Control.

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<PAGE>
 
                        THE CARBIDE/GRAPHITE GROUP, INC.

                  NON EMPLOYEE DIRECTOR STOCK-BASED INCENTIVE
                               COMPENSATION PLAN
                          (Effective August 26, 1996)

                               TABLE OF CONTENTS
                               -----------------

<TABLE>
<C>  <S>                                         <C>

1.   Purpose of the Plan........................  1

2.   Definitions................................  1

     2.1.  "Affiliate"..........................  1
     2.2.  "Award"..............................  1
     2.3.  "Board"..............................  1
     2.4.  "Change in Control"..................  1
     2.5.  "Code"...............................  1
     2.6.  "Common Stock".......................  2
     2.7.  "Company"............................  2
     2.8.  "Committee"..........................  2
     2.9.  "Disability".........................  2
     2.10.  "Non Employee Director".............  2
     2.11.  "Fair Market Value".................  2
     2.12.  "Holder"............................  2
     2.13.  "1934 Act"..........................  2
     2.14.  "Non Qualified Option"..............  2
     2.15.  "Option"............................  2
     2.16.  "Plan"..............................  2
     2.17.  "Subsidiary"........................  3

3.   Eligibility................................  3

4.   Administration of Plan.....................  3

5.   Grants of Awards Under the Plan............  3

     5.1.  Grant of Awards......................  3
     5.2.  No Reduction in Shares...............  3
     5.3.  Restriction on Transferability.......  4
     5.4.  Payment of Option Price..............  4
     5.5.  Termination by Death.................  4
     5.6.  Termination by Reason of Disability..  4
     5.7.  Other Termination....................  4

6.   Adjustments Upon Changes in Capitalization.  4

</TABLE>

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<TABLE>
 
<C>    <S>                                         <C>

 7.    Effective Date, Termination and Amendment... 5

 8.    Execution and Delivery of Stockholders
       Agreement................................... 5

 9.    Non-Assignability........................... 5

10.    General Provisions.......................... 5

10.1.  No Right to Position........................ 5

10.2.  Governing Law............................... 5

10.3.  Compliance with Law......................... 5
 
11.    Change in Control........................... 6

</TABLE>

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