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                                                                    EXHIBIT 10.4

                                 KENNAMETAL INC.

                             STOCK OPTION AGREEMENT

                    DATE OF GRANT OF THIS OPTION: MAY 4, 1999

         THIS AGREEMENT made by and between KENNAMETAL INC., a Pennsylvania
corporation (hereinafter called the "Company"), and Markos I. Tambakeras
(hereinafter called the "Optionee") is made as of the above date under the
Kennametal Inc. 1999 Stock Option Plan (the "Plan").

                                   WITNESSETH:

         1. The Company grants to the Optionee a Nonstatutory Stock Option (the
"Option") to purchase 35,000 shares of the $1.25 Par Value Capital Stock of the
Company at the price of $ 38.00 per share, subject to the terms and conditions
of the Plan, except as expressly provided in the Agreement.

         2. The Option must be exercised within ten (10) years from July 1,
1999, and only at the times and for the number of shares indicated as follows:
(a) prior to June 30, 2000, this Option is not exercisable as to any shares; (b)
on June 30, 2000, this Option shall become exercisable as to 11,667 shares; (c)
on June 30, 2001, this Option shall become exercisable as to 11,667 shares; and
(d) on June 30, 2002, this Option shall become exercisable as to the remaining
11,666 shares.

         3. In addition to the vesting provisions stated in the Plan, the Shares
subject to this Agreement shall immediately vest upon termination of Employee
without Cause or upon Employee's termination of employment due to an Employer's
Breach, or upon a Change-in-Control, all as defined in Employee's Executive
Employment Agreement dated as of May 4, 1999.

         4. It is intended that the Option not constitute an Incentive Stock
Option under Section 422 of the Internal Revenue Code of 1986, as amended (the
"Code").

         5. The Optionee or any purchaser permitted to purchase the shares
pursuant to the terms of the Plan shall purchase not less than 100 shares at any
one purchase (or the total number of shares purchasable under this Option at
such time, if less than 100).

         6. If the Optionee shall cease to be employed by the Company or any of
its subsidiaries, the Option will continue its normal vesting period as provided
above, unless such termination of employment shall be for Cause (as defined in
Optionee's Executive Employment Agreement dated as of May 4, 1999) or in
violation of an agreement by the Optionee to remain in the employ of the Company
or one of its subsidiaries, in which case the Option shall forthwith terminate;
provided however, that the Plan Administrator may in its sole discretion extend
the


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option period of any option for up to three years from the date of termination
of employment regardless of the original option period.

         7. The Option may be exercised only by written request to the Treasurer
of the Company at Latrobe, Pennsylvania, accompanied by payment of the option
price in full either (i) in cash for the shares with respect to which it is
exercised, (ii) by delivering to the Company a notice of exercise with an
irrevocable direction to a registered broker-dealer under the Securities
Exchange Act of 1934, as amended, to sell a sufficient portion of the shares and
deliver the sale proceeds directly to the Company, (iii) by delivering shares of
the $1.25 Par Value Capital Stock ("Capital Stock") of the Company; provided
however that the shares of Capital Stock delivered in payment of the option
price must have been held by the participant for at least six (6) months in
order to be utilized to pay the option price; or (iv) a combination of payment
procedures set forth above.

         8. The Optionee may pay the Company the amount required to be withheld
under applicable tax withholding requirements (i) in cash; (ii) through the
delivery to the Company of previously owned shares of Capital Stock having an
aggregate fair market value on the Tax Date equal to the tax obligation; or
(iii) through any combination of payment procedures set forth in subsections
(i)-(ii). Tax withholding obligations may not be satisfied by withholding shares
of Capital Stock otherwise issuable in connection with an exercise of the
Option.

         9. Each capitalized term used herein without being defined herein shall
have the meaning ascribed to it in the Plan.

         IN WITNESS WHEREOF, the undersigned have executed this Stock Option
Agreement as of the date first above written.

EXECUTED IN DUPLICATE

ATTEST:                               KENNAMETAL INC.


/s/ David T. Cofer                    By: /s/ Timothy D. Hudson
- ----------------------------              -------------------------------
         Secretary                                Vice President


WITNESS:                              Optionee:


/s/ Nancy Torba                       /s/  Markos I. Tambakeras
- ----------------------------              -------------------------------
                                               Markos I. Tambakeras