content: SECURITIES AND EXCHANGE COMMISSION
                            Washington, DC  20549
                            _________________
                                 FORM 144
                   NOTICE OF PROPOSED SALE OF SECURITIES
              PURSUANT TO RULE 144 UNDER THE SECURITIES ACT OF 1933
  
  ATTENTION:   Transmit for filing 3 copies of this form concurrently with
  either placing an order with a broker to execute sale or executing a sale
  directly with a market maker.
  
  1(a)  NAME OF ISSUER (Please type or print)
        Valero Energy Corporation
   (b)  IRS IDENT. NO.
        74-1828067
   (c)  S.E.C. FILE NO.
        1-13175
  1(d)  ADDRESS OF ISSUER
        STREET
        7990 IH 10 West
        CITY
        San Antonio
        STATE
        TX
        ZIP CODE
        78230
   (e) TELEPHONE NO.
       AREA CODE
       210
       NUMBER
       370-2000
  
  2(a)  NAME OF PERSON FOR WHOSE ACCOUNT THE SECURITIES ARE TO BE SOLD
        S. Eugene Edwards
   (b)  IRS IDENT. NO.
        ###-##-####
   (c)  RELATIONSHIP TO ISSUER
        Vice President
   (d)  ADDRESS
  
        STREET
        7990 IH 10 West
        CITY
        San Antonio
        STATE
        TX
        ZIP CODE
        78230
  
  INSTRUCTION:  The person filing this notice should contact the issuer to
  obtain the I.R.S. Identification Number and the S.E.C. File Number
  
  3(a) Title of the Class of Securities To Be Sold
       Common Stock
   (b) Name And Address Of Each Broker Through Whom The Securities
       Are To Be Offered Or Each Market Maker Who Is Acquiring The
       Securities
       Fidelity Investments
       82 Devonshire Street
       Boston, MA  02109
  
       SEC USE ONLY
       Broker-Dealer File Number
  
   (c) Number of Shares Or Other Units To Be Sold (See Instr. 3(c))
       1,107
   (d) Aggregate Market Value (See Instr. 3(d))
       $36,323.44
   (e) Number Of Shares Or Other Units Outstanding (See Instr. 3(e))
       56,195,070
   (f) Approximate Date Of Sale (see Instr. 3(f)) (MO. DAY YR.)
       06/30/98
   (g) Name of Each Securities Exchange (See Instr. 3(g))
       NYSE
  
  INSTRUCTIONS:
  1. (a) Name of issuer.
     (b) Issuer's I.R.S. Identification Number.
     (c) Issuer's S.E.C. file number, if any.
     (d) Issuer's address, including zip code.
     (e) Issuer's telephone number, including area code.
  
  2. (a) Name of person for whose account the securities are to be sold.
     (b) Such person's I.R.S. identification number, if such person is
         an entity.
     (c) Such person's relationship to the issuer (e.g., officer,
         director, 10 percent stockholder, or member of immediate family
         of any of the foregoing).
     (d) Such person's address, including zip code.
  
  3. (a) Title of the class of securities to be sold
     (b) Name and address of each broker through whom the securities
         are intended to be sold.
     (c) Number of shares or other units to be sold (if debt securities,
         give the aggregate face amount).
     (d) Aggregate market value of the securities to be sold as of a
         specified date within 10 days prior to the filing of this notice.
     (e) Number of shares or other units of the class outstanding, or if
         debt securities the face amount thereof outstanding, as shown
         by the most recent report or statement published by the issuer.
     (f) Approximate date on which the securities are to be sold.
     (g) Name of each securities exchange, if any, on which the
         securities are intended to be sold.
  
                   TABLE I   SECURITIES TO BE SOLD
     Furnish the following information with respect to the acquisition of the
  securities to be sold and with respect to the payment of all or any part of
  the purchase price or other consideration therefor:
  
  <TABLE>
  <CAPTION>
                                                         Name of Person From             Amount of
  Title of       Date You     Nature of                  Whom Acquired (If Gift,         Securities   Date of    Nature of
  The Class      Acquired     Acquisition Transaction    Also Give Date Donor Acquired)  Acquired     Payment    Payment
  <S>            <C>          <C>                        <C>                             <C>          <C>        <C>
  Common Stock   06/19/97     Restricted Stock Grant     Valero Energy Corporation       1,107        n/a        n/a
  
  </TABLE>
  
  INSTRUCTIONS:
  1. If the securities were purchased and full payment therefor was not made in
  cash at the time of purchase, explain in the table or in a note thereto the
  nature of the consideration given.  If the consideration consisted of any note
  or other obligation, or if payment was made in installments describe the
  arrangement and state when the note or other obligation was discharged in full
  or the last installment paid.
  
  2. If within two years after the acquisition of the securities the person for
  whose account they are to be sold had any short positions, put or other option
  to dispose of securities referred to in paragraph (d)(3) of Rule 144, furnish
  full information with respect thereto.
  
          TABLE II   SECURITIES SOLD DURING THE PAST THREE MONTHS
  
  Furnish the following information as to all securities of the issuer sold
  during the past three months by the person for whose account the securities
  are to be sold.
  
  <TABLE>
  <CAPTION>
  Name And              Title of                             Amount of           Gross
  Address Of Seller     Securities Sold     Date Of Sale     Securities Sold     Proceeds
  <S>                   <C>                 <C>              <C>                 <C>
  
  None
  
  </TABLE>
  
  REMARKS:
  
  INSTRUCTIONS:
  See the definition of "person" in paragraph (a) of Rule 144.  Information is
  to be given not only as to the person for whose account the securities are to
  be sold but also as to all other persons included in that definition.  In
  addition, information shall be given as to sales by all persons whose sales
  are required by paragraph (e) of Rule 144 to be aggregated with sales for the
  account of the person filing this notice.
  
  ATTENTION:
  The person for whose account the securities to which this notice relates are
  to be sold hereby represents by signing this notice that he does not know any
  material adverse information in regard to the current and prospective
  operations of the Issuer of the securities to be sold which has not been
  publicly disclosed.
  <PAGE>
     06/30/98                                /s/ S. Eugene Edwards
  (DATE OF NOTICE)                                 (SIGNATURE)
                                               S. Eugene Edwards
  
  The notice shall be signed by the person for whose account the
  securities are to be sold.  At least one copy of the notice shall
  be manually signed. Any copies not manually signed shall bear typed
  or printed signatures.
  
  ATTENTION:  Intentional misstatements or omission of facts constitute
  Federal Criminal Violations.  (See U.S.C. 1001.)
metadata_documents: [{"type": "144", "sequence": "1", "description": "S EUGENE EDWARDS - FORM 144", "secsgml_size_bytes": 6758}]
text: SECURITIES AND EXCHANGE COMMISSION
                            Washington, DC  20549
                            _________________
                                 FORM 144
                   NOTICE OF PROPOSED SALE OF SECURITIES
              PURSUANT TO RULE 144 UNDER THE SECURITIES ACT OF 1933
  
  ATTENTION:   Transmit for filing 3 copies of this form concurrently with
  either placing an order with a broker to execute sale or executing a sale
  directly with a market maker.
  
  1(a)  NAME OF ISSUER (Please type or print)
        Valero Energy Corporation
   (b)  IRS IDENT. NO.
        74-1828067
   (c)  S.E.C. FILE NO.
        1-13175
  1(d)  ADDRESS OF ISSUER
        STREET
        7990 IH 10 West
        CITY
        San Antonio
        STATE
        TX
        ZIP CODE
        78230
   (e) TELEPHONE NO.
       AREA CODE
       210
       NUMBER
       370-2000
  
  2(a)  NAME OF PERSON FOR WHOSE ACCOUNT THE SECURITIES ARE TO BE SOLD
        S. Eugene Edwards
   (b)  IRS IDENT. NO.
        ###-##-####
   (c)  RELATIONSHIP TO ISSUER
        Vice President
   (d)  ADDRESS
  
        STREET
        7990 IH 10 West
        CITY
        San Antonio
        STATE
        TX
        ZIP CODE
        78230
  
  INSTRUCTION:  The person filing this notice should contact the issuer to
  obtain the I.R.S. Identification Number and the S.E.C. File Number
  
  3(a) Title of the Class of Securities To Be Sold
       Common Stock
   (b) Name And Address Of Each Broker Through Whom The Securities
       Are To Be Offered Or Each Market Maker Who Is Acquiring The
       Securities
       Fidelity Investments
       82 Devonshire Street
       Boston, MA  02109
  
       SEC USE ONLY
       Broker-Dealer File Number
  
   (c) Number of Shares Or Other Units To Be Sold (See Instr. 3(c))
       1,107
   (d) Aggregate Market Value (See Instr. 3(d))
       $36,323.44
   (e) Number Of Shares Or Other Units Outstanding (See Instr. 3(e))
       56,195,070
   (f) Approximate Date Of Sale (see Instr. 3(f)) (MO. DAY YR.)
       06/30/98
   (g) Name of Each Securities Exchange (See Instr. 3(g))
       NYSE
  
  INSTRUCTIONS:
  1. (a) Name of issuer.
     (b) Issuer's I.R.S. Identification Number.
     (c) Issuer's S.E.C. file number, if any.
     (d) Issuer's address, including zip code.
     (e) Issuer's telephone number, including area code.
  
  2. (a) Name of person for whose account the securities are to be sold.
     (b) Such person's I.R.S. identification number, if such person is
         an entity.
     (c) Such person's relationship to the issuer (e.g., officer,
         director, 10 percent stockholder, or member of immediate family
         of any of the foregoing).
     (d) Such person's address, including zip code.
  
  3. (a) Title of the class of securities to be sold
     (b) Name and address of each broker through whom the securities
         are intended to be sold.
     (c) Number of shares or other units to be sold (if debt securities,
         give the aggregate face amount).
     (d) Aggregate market value of the securities to be sold as of a
         specified date within 10 days prior to the filing of this notice.
     (e) Number of shares or other units of the class outstanding, or if
         debt securities the face amount thereof outstanding, as shown
         by the most recent report or statement published by the issuer.
     (f) Approximate date on which the securities are to be sold.
     (g) Name of each securities exchange, if any, on which the
         securities are intended to be sold.
  
                   TABLE I   SECURITIES TO BE SOLD
     Furnish the following information with respect to the acquisition of the
  securities to be sold and with respect to the payment of all or any part of
  the purchase price or other consideration therefor:
  Name of Person From             Amount of
  Title of       Date You     Nature of                  Whom Acquired (If Gift,         Securities   Date of    Nature of
  The Class      Acquired     Acquisition Transaction    Also Give Date Donor Acquired)  Acquired     Payment    Payment
  Common Stock   06/19/97     Restricted Stock Grant     Valero Energy Corporation       1,107        n/a        n/a
  INSTRUCTIONS:
  1. If the securities were purchased and full payment therefor was not made in
  cash at the time of purchase, explain in the table or in a note thereto the
  nature of the consideration given.  If the consideration consisted of any note
  or other obligation, or if payment was made in installments describe the
  arrangement and state when the note or other obligation was discharged in full
  or the last installment paid.
  
  2. If within two years after the acquisition of the securities the person for
  whose account they are to be sold had any short positions, put or other option
  to dispose of securities referred to in paragraph (d)(3) of Rule 144, furnish
  full information with respect thereto.
  
          TABLE II   SECURITIES SOLD DURING THE PAST THREE MONTHS
  
  Furnish the following information as to all securities of the issuer sold
  during the past three months by the person for whose account the securities
  are to be sold.
  Name And              Title of                             Amount of           Gross
  Address Of Seller     Securities Sold     Date Of Sale     Securities Sold     Proceeds
  None
  REMARKS:
  
  INSTRUCTIONS:
  See the definition of "person" in paragraph (a) of Rule 144.  Information is
  to be given not only as to the person for whose account the securities are to
  be sold but also as to all other persons included in that definition.  In
  addition, information shall be given as to sales by all persons whose sales
  are required by paragraph (e) of Rule 144 to be aggregated with sales for the
  account of the person filing this notice.
  
  ATTENTION:
  The person for whose account the securities to which this notice relates are
  to be sold hereby represents by signing this notice that he does not know any
  material adverse information in regard to the current and prospective
  operations of the Issuer of the securities to be sold which has not been
  publicly disclosed.
  06/30/98                                /s/ S. Eugene Edwards
  (DATE OF NOTICE)                                 (SIGNATURE)
                                               S. Eugene Edwards
  
  The notice shall be signed by the person for whose account the
  securities are to be sold.  At least one copy of the notice shall
  be manually signed. Any copies not manually signed shall bear typed
  or printed signatures.
  
  ATTENTION:  Intentional misstatements or omission of facts constitute
  Federal Criminal Violations.  (See U.S.C. 1001.)