<PAGE>
 
                                                                   EXHIBIT 10.20





                                 April 16, 1997

Mr. Ronald N. Clawson
The Carbide/Graphite Group, Inc.
One Gateway Center
Pittsburgh, Pennsylvania 15222

Dear Ron:

          We refer to your employment agreement with The Carbide/Graphite Group,
Inc. (the "Corporation") dated March 31, 1995 (the "Employment Agreement"). This
letter will serve to confirm our understanding regarding the termination of your
employment with the Corporation, as follows:

     1. Termination of Employment Agreement. The Employment Agreement is hereby
        -----------------------------------
terminated in its entirety and shall no longer have any force or effect. You
hereby resign as an officer of the Corporation, its affiliates, subsidiaries and
business units, and as a director of the Corporation, effective as of April 30,
1997.

     2. Severance; Consulting. For a period of 24 consecutive months commencing
        ---------------------
May 1, 1997, the Corporation shall pay to you on the first day of each such
month the sum $19,917, less any required withholding under applicable law. The
Corporation may make such payments on a bimonthly basis if it so elects. If
requested by the Corporation during such 24-month period and in consideration of
the payments provided for in this Section 2, you will be available for
consultation regarding the Corporation's operations and activities (including
the Carbide
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October 27, 1997
Page 2
 
Products business unit, from time to time at a mutually acceptable time and
place. You will be reimbursed for any out-of-pocket costs incurred by you and
necessitated by any travel.

     3. Bonus; Profit Sharing. You shall not be entitled to a bonus pursuant to
        ---------------------
the Corporation's Annual Incentive Bonus Compensation Plan for the current
fiscal year ending July 31, 1997 (the "1997 Fiscal Year"), but you shall be
entitled to receive your pro rata profit sharing benefit for the current 1997
Fiscal Year under the Corporation's Savings Investment Plan for the period
through April 30, 1997. Of course, you shall be entitled to your vested benefits
under the Corporation's Compensation Deferral Plan in accordance with the terms
of such Plan.

     4. Insurance Benefits. For a period of 24 months commencing May 1, 1997,
        ------------------
the Corporation shall afford to you at its expense health insurance benefits
(including medical and dental) and life insurance equivalent to the benefits
enjoyed by you on the date hereof.

     5. Stock Options. You currently hold options to purchase 20,000 shares of
        -------------
the Corporation's common stock at an exercise price of $2.00 per share pursuant
to the Corporation's 1991 Stock Option Plan, which options expire in September
1998 and are fully vested and exercisable. Pursuant to the provisions of the
Stock Option Plan such options shall terminate on the seventh anniversary of the
date of grant (September 23, 1998) and you shall be entitled to exercise such
options until such date. The stock options granted to you in 1996 pursuant to
the 1995 Stock Option Plan are hereby terminated.

     6. Release. You acknowledge that, other than as set forth herein, you have
        -------
no other claims against the Corporation, and you are concurrently herewith
executing the Release attached hereto as Attachment I.
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October 27, 1997
Page 3
 
     7.  Confidentiality; Non-Compete.  You hereby agree to be bound by the
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confidentiality provisions set forth in Attachment II (paragraphs (a), (c) and
(d)) for a period of three years from the date hereof and the non-competition
provisions set forth in Attachment II (paragraphs (b), (c) and (d)) for a period
of two years from the date hereof.

     8. Successors. (a) This letter agreement is personal to you and without the
        ---------- 
prior written consent of the Corporation shall not be assignable by you other
than by will or the laws of descent and distribution.

     b) This letter agreement shall inure to the benefit of and be binding upon
the Corporation and its successors.

     9.  Miscellaneous.  (a)  This letter agreement shall be governed by and
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construed in accordance with the laws of the State of Delaware, without
reference to principles of conflict of laws.
 
     (b)  All notices and other communications hereunder shall be in writing and
shall be given by hand delivery to the other party or by registered or certified
mail, return receipt requested, postage prepaid, addressed as follows:


              If to you:

              Ronald N. Clawson
              1703 Sturbridge Drive
              Sewickley, Pennsylvania 15143
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October 27, 1997
Page 4
 
              If to the Corporation:

              The Carbide/Graphite Group, Inc.
              One Gateway Center, 19th Floor
              Pittsburgh, Pennsylvania  15222

              Attention: Secretary

or to such other address as either party shall have furnished to the other in
writing in accordance herewith. Notices and communications shall be effective
when actually received by the addressee.

     (c) The Corporation may withhold from any amounts payable under this letter
agreement such Federal, state or local taxes as shall be required to be withheld
pursuant to any applicable law or regulation.

     (d) The Corporation's failure to insist upon strict compliance with any
provision hereof shall not be deemed to be a waiver of such provision or any
other provision hereof.

Your failure to insist upon strict compliance with any provision hereof shall
not be deemed to be a waiver of such provision or any other provision hereof.

     (e) This letter agreement embodies the entire agreement between the parties
with respect to the subject matter hereof and may not be changed or terminated
orally.

     (f)  At your request, the Corporation will pay, or reimburse you for, the
reasonable charges of an outplacement service.

     10. Counsel. You acknowledge that you have consulted with independent legal
         -------
counsel (other than counsel acting for the Corporation) or have had the
opportunity to consult such counsel but declined to do so, in connection with
the negotiation and execution of this agreement.
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October 27, 1997
Page 5
 
     11. No Disparagement. The Corporation and you each agree not to disparage
         ---------------- 
the other; provided that the Corporation and its directors and you may take
such actions as may be required by applicable law or to enforce this Agreement
or to defend against a claim related thereto or, in the case of the directors
of the Corporation, to satisfy their fiduciary responsibilities.

     12. Confidentiality. The parties hereto shall not divulge the terms of this
         ---------------
agreement to third parties generally, for any purpose detrimental to the
Corporation, except as required by applicable law or to enforce this Agreement
or to defend against a claim related thereto and except that the Corporation may
reveal such terms to its stockholders, financing sources, accountants, legal
counsel, directors and management employees and such other parties as the
Corporation's Board of Directors in good faith shall deem necessary or
desirable.

          If the foregoing correctly sets forth our understanding, please
execute one copy of this letter agreement and return it to the Corporation, at
which time it shall be a binding agreement between you and the Corporation.

                                       Very truly yours,

                                       THE CARBIDE/GRAPHITE GROUP, INC.

                                       By:    /s/ Walter B. Fowler
                                         -------------------------------------- 


Accepted and Agreed:

     /s/ Ronald N. Clawson
----------------------------------
Ronald N. Clawson
<PAGE>
 
                                 ATTACHMENT II
                                 -------------

                   Confidential Information; Non-Competition
                   -----------------------------------------

     (a) You agree that (i) you shall hold in a fiduciary capacity for the
benefit of the Corporation all secret or confidential information, knowledge or
data relating to the Corporation or its affiliates, and their respective or
former businesses which shall not be public knowledge (which term shall not
include information which becomes public as a result of your act or acts of your
representatives in violation of this Agreement), including, without limitation,
customer lists, bid proposals, contracts, matters subject to litigation,
technology or financial information of the Corporation or its subsidiaries,
confidential information received from third parties with whom the Corporation
has business relationships, and other know-how, and (ii) you shall not, without
the prior written consent of the Corporation, communicate or divulge any such
information, knowledge or data to anyone other than the Corporation and those
designated by it in writing.


     (b) Without the prior written approval of the Corporation, you agree that
you will not, directly or indirectly, (i) own, manage, operate, control or
participate in the ownership, management or control of, or be connected as an
officer, employee, partner, director, or consultant or otherwise with, or have
any financial interest in (except for (A) ownership as of the date hereof, (B)
any ownership in the common stock of the Corporation, or (C) any ownership of
less than 5% of the outstanding equity interest) any entity engaged in (I) the
manufacture of graphite electrodes, (II) the manufacture of calcium carbide and
specialty graphite products, or (III) the refining of products required for the
production of, or the production of, needle coke, or the manufacture or
marketing of calcium carbide, calcium carbide desulfurizing products, calcium
carbide used in metallurgical applications and calcium hydrate or (IV) the
manufacture or marketing of any products which compete with any of the
Corporation's principle product lines currently offered for sale in the markets
in which the Corporation presently solicits business or (ii) solicit or contact
any employee of the Corporation or its affiliates with a view to inducing or
encouraging such employee to leave the employ of the Corporation or its
affiliates for the purpose of being employed by you, an employer affiliated with
you, or any competitor of the Corporation or any affiliate thereof.

     (c) You acknowledge that the provisions of this Attachment II are
reasonable and necessary for the protection of the Corporation and that the
Corporation will be irrevocably damaged if such provisions are not specifically
enforced. Accordingly, you agree that, in addition to any other relief to which
the Corporation may be entitled in the form of actual or punitive damages, the
Corporation shall be entitled to seek and obtain injunctive relief from a court
of competent jurisdiction (without the posting of a bond therefor) for the
purposes of restraining you from any actual or threatened breach of such
provisions.

     (d) Although the restrictions contained in this Attachment II are
considered by the parties hereto be fair and reasonable in the circumstances, it
is recognized that restrictions of


                                     II-1
<PAGE>
 
the nature contained in this Attachment II may fail for technical reasons, and
accordingly if any of such restrictions shall be adjudged to be void or
unenforceable for whatever reason, but would be valid if part of the wording
thereof were deleted, or the period thereof reduced or the area dealt with
thereby reduced in scope, the restrictions contained in this Attachment shall
apply, at the election of the Corporation, with such modifications as may be
necessary to make them valid, effective and enforceable in the particular
jurisdiction in which such restrictions are adjudged to be void and
unenforceable.

                                     II-2
<PAGE>
 
                                General Release
                                ---------------

          Notice:  This is a very important legal document and you should
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carefully review and understand the terms and effect of this document before
signing it. By signing this General Release you are agreeing to completely
release the Company from all liability to you. Therefore, you should consult
with an attorney before signing the General Release. You have 21 days from the
date of the distribution of this document to consider this document. if you have
not returned a signed copy of the General Release by that time, we will assume
that you have elected not to sign the General Release. If you choose to sign the
General Release, you will have an additional 7 days following the date of your
signature to revoke the agreement and the agreement shall not become effective
or enforceable until the revocation period has expired.

          In consideration of benefits to which I would not otherwise be
entitled offered to me by The Carbide/Graphite Group, Inc., I hereby release and
discharge The Carbide/Graphite Group, Inc., and their affiliates, parents,
subsidiaries, successors, and predecessors, and all of their employees, agents,
officers and directors (hereinafter collectively referred to as "the Company")
from any and all claims and/or causes of action, known or unknown, which I may
have or could claim to have against the Company up to and including the date of
my signing of this General Release. This General Release includes, but is not
limited to, all claims arising from or during my employment or as a result of
the termination of my employment and all claims arising under federal, state or
local laws prohibiting employment discrimination based upon age, race, sex,
religion, handicap, national origin or any other protected characteristic,
including, but not limited to, any and all claims arising under the Age
Discrimination in Employment Act, Title VII of the Civil Rights Act of 1964,
and/or claims growing out of any legal restrictions, expressed or implied, on
the Company's right to control or terminate the employment of its employees.

          By signing below, I acknowledge that I have carefully read and fully
understand the provisions of this General Release. I further acknowledge that I
am signing this General Release knowingly and voluntarily and without duress,
coercion or undue influence. I further agree that should I file a lawsuit in
court which is found to be barred in whole or part by this General Release, I
will pay the legal fees incurred by the Company in defending those claims found
to be barred. This Agreement constitutes the total and complete understanding
between me and the Company relating to the subject matter covered by this
General Release, and all other prior or contemporaneous written or oral
agreements or representations, if any, relating to the subject matter of this
General Release are null and void. It is also expressly understood and agreed
that the terms of this General Release may not be altered except in a writing
signed by both me and the Company.


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INTENDING TO BE LEGALLY BOUND, I hereby set my hand below:

WITNESSED BY:


     /s/ Walter E. Damian                   /s/ Ronald N. Clawson
----------------------------------    -------------------------------------


Dated:         4/25/97                Dated:       4/25/97
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