UNITED STATES SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549
FORM 4
STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP
( ) Check this box if no longer subject to Section 16.
Form 4 or Form 5 obligations may continue. See Instructions 1(b).
1. Name and Address of Reporting Person
   Calgaard, Ronald K.
   One Valero Place
   San Antonio, TX  78212
   USA
2. Issuer Name and Ticker or Trading Symbol
   Valero Energy Corporation
   VLO
3. IRS or Social Security Number of Reporting Person (Voluntary)

4. Statement for Month/Year
   05/31/02
5. If Amendment, Date of Original (Month/Year)

6. Relationship of Reporting Person(s) to Issuer (Check all applicable)
   (X) Director ( ) 10% Owner ( ) Officer (give title below) ( ) Other
   (specify below)
   Director
7. Individual or Joint/Group Filing (Check Applicable Line)
   (X) Form filed by One Reporting Person
   ( ) Form filed by More than One Reporting Person


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 Table I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned                                                 |
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1. Title of Security       |2.    |3.    |4.Securities Acquired (A)         |5.Amount of        |6.Dir |7.Nature of Indirect       |
                           | Transaction |  or Disposed of (D)              |  Securities       |ect   |  Beneficial Ownership     |
                           |      |      |                                  |  Beneficially     |(D)or |                           |
                           |      |    | |                  | A/|           |  Owned at         |Indir |                           |
                           | Date |Code|V|    Amount        | D |    Price  |  End of Month     |ect(I)|                           |
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Common Stock ($0.01 par val|05/09/|A   |V|1,095 (1)         |A  |           |3,945              |D     |                           |
ue)                        |02    |    | |                  |   |           |                   |      |                           |
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(1) See footnote (1) on Tab|      |    | |                  |   |           |                   |      |                           |
le II.                     |      |    | |                  |   |           |                   |      |                           |
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 Table II -- Derivative Securitites Acquired, Disposed of, or Beneficially Owned                                                   |
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1.Title of Derivative |2.Con-  |3.   |4.    |5.Number of De |6.Date Exer|7.Title and Amount  |8.Price|9.Number    |10.|11.Nature of|
  Security            |version |Transaction | rivative Secu |cisable and|  of Underlying     |of Deri|of Deriva   |Dir|Indirect    |
                      |or Exer |     |      | rities Acqui  |Expiration |  Securities        |vative |tive        |ect|Beneficial  |
                      |cise    |     |      | red(A) or Dis |Date(Month/|                    |Secu   |Securities  |(D)|Ownership   |
                      |Price of|     |      | posed of(D)   |Day/Year)  |                    |rity   |Benefi      |or |            |
                      |Deriva- |     |      |               |Date |Expir|                    |       |ficially    |Ind|            |
                      |tive    |     |      |           | A/|Exer-|ation|   Title and Number |       |Owned at    |ire|            |
                      |Secu-   |     |    | |           | D |cisa-|Date |   of Shares        |       |End of      |ct |            |
                      |rity    |Date |Code|V|  Amount   |   |ble  |     |                    |       |Month       |(I)|            |
___________________________________________________________________________________________________________________________________|
                                                                            
Stock Option (right to|$41.12  |05/09|A   |V|2,000      |A  |11/09|05/09|Common Stock|2,000  |       |2,000       |D  |            |
 buy)                 |        |/02  |    | |           |   |/02  |/12  |            |       |       |            |   |            |
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                      |        |     |    | |           |   |     |     |            |       |       |            |   |            |
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Explanation of Responses:
(1) Award of restricted stock under the Valero Energy Corporation Non-Employee
Director Restricted Stock Plan.  The shares of restricted stock vest
incrementally over a three-year period beginning in
2003.
SIGNATURE OF REPORTING PERSON
J. Stephen Gilbert, Attorney-in-Fact for Ronald K. Calgaard
DATE
06/04/02