
<PAGE>
 
                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                                 SCHEDULE 13D

                   Under the Securities Exchange Act of 1934

                            (Amendment No. ______)*

                              AccelGraphics, Inc.
                              -------------------
                               (Name of Issuer)

                    Common Stock par value $.001 per share
                    --------------------------------------
                        (Title of Class of Securities)

                                  00430P 10 4
                                  -----------
                                (CUSIP Number)



             David K. Armstrong              Edmund S. Ruffin, Jr.
           Snell & Wilmer, L.L.P.             Venture Law Group
               Broadway Centre            A Professional Corporation
        111 East Broadway, Suite 900         2800 Sand Hill Road
        Salt Lake City, Utah 84111      Menlo Park, California 94025
              (801)237-1900                      (650)854-4488

                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                                April 22, 1998
                                --------------
            (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(b)(3) or (4), check the following box [_].

* The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).
<PAGE>
 
                                      13D
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 2 of 10 Pages
________________________________________________________________________________
1       NAME OF REPORTING PERSON
        SS. or I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
        EVANS & SUTHERLAND COMPUTER CORPORATION
        EIN: 87-0278175
________________________________________________________________________________
2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A
        GROUP                                                           (a)  [_]
                                                                        (b)  [_]
________________________________________________________________________________
3       SEC USE ONLY

________________________________________________________________________________
4       SOURCE OF FUNDS
        WC
________________________________________________________________________________
5       CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS
        REQUIRED
        PURSUANT TO ITEM 2(d) OR 2(e)                                        [_]
________________________________________________________________________________
6       CITIZENSHIP OR PLACE OF ORGANIZATION
        UTAH
________________________________________________________________________________
                      7   SOLE VOTING POWER
                          3,159,963 
                      __________________________________________________________
NUMBER OF SHARES      8   SHARED VOTING POWER  
BENEFICIALLY              3,159,963                
OWNED BY EACH         __________________________________________________________
REPORTING             9   SOLE DISPOSITIVE POWER  
PERSON WITH               -0-                         
                      __________________________________________________________
                      10  SHARED DISPOSITIVE POWER
                          -0-                         
________________________________________________________________________________
11      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
        REPORTING PERSON
        3,159,963
________________________________________________________________________________
12      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11)
        EXCLUDES CERTAIN SHARES*  [_]
________________________________________________________________________________
13      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW
        (11)
        37.4%
________________________________________________________________________________
14      TYPE OF REPORTING PERSON*
        CO
________________________________________________________________________________
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 3 of 10 Pages
________________________________________________________________________________


ITEM 1.   SECURITY AND ISSUER.

     The title of the class of equity securities to which this statement relates
is the common stock, $.001 par value per share, of AccelGraphics, Inc., a
Delaware corporation (the "Issuer").  The Issuer's principal executive office is
located at 1873 Barber Lane, Milpitas, CA  95035.


ITEM 2.   IDENTITY AND BACKGROUND.
 
     This Schedule 13D is filed by Evans & Sutherland Computer Corporation
("E&S"), a Utah corporation.  E&S's address is 600 Komas Drive, Salt Lake City,
Utah 84108.  To the best of E&S's knowledge, during the last five years, neither
E&S nor any of its executive officers or directors has been convicted in a
criminal proceeding (excluding traffic violations or similar misdemeanors) or
has been a party to a civil proceeding of a judicial or administrative body of
competent jurisdiction resulting in a judgment, decree or final order enjoining
future violations of, or prohibiting or mandating activities subject to, federal
or state securities laws, or finding any violation with respect to such laws.

     The name, business address, present principal occupation (including the
name and address of the corporation or organization in which such employment is
conducted) and, citizenship of each executive officer and director of E&S is set
forth in Schedule A to this Schedule 13D and is specifically incorporated herein
by reference in its entirety.

ITEM 3.   SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

     This Statement relates to a voting agreement and associated proxy granted
to E&S by Stephen L. Bartlett, Nancy E. Bush, Jeffrey W. Dunn, Lew S. Epstein,
David W. Pidwell, Niraj Swarup, Arthur Yan, Advanced Technology Ventures IV,
L.P., STF II, L.P., Asset Management Associates 1996, L.P., AVI Capital, L.P.,
Associated Venture Investors II, L.P., AVI Partners Growth Fund II, L.P., and
AVI Silicon Valley Partners, L.P. (the "Stockholders") with regard to their
shares of Common Stock of the Issuer as described in Item 6 below.  The voting
agreement and associated proxy were granted  to E&S by the Stockholders pursuant
to the Voting Agreement and Irrevocable Proxy dated April 22, 1998 among E&S and
the Stockholders (the "Voting Agreement").

     Pursuant to the Voting Agreement, the Stockholders have agreed to vote
their shares of Common Stock of the Issuer (i) in favor of the Merger, (ii)
against any action that would constitute a breach of the Merger Agreement or the
Voting Agreement and (iii) against any action that could interfere with the
transactions contemplated by the Merger Agreement, including, without
limitation, any competing business combination, all as more fully described in,
and under the circumstances set forth in, the Voting Agreement; provided,
however, that the Stockholders are not required to vote in favor of the Merger
if the Board of Directors of the Issuer has determined that the Issuer has
received a Superior Proposal (as such term is defined in the Merger Agreement)
from a third party.  In addition, pursuant to the Voting Agreement, each of the
Stockholders has granted E&S an irrevocable proxy to vote their respective
shares of Common Stock if they fail to comply with their obligation to vote
their shares of Common Stock in the manner required by the Voting Agreement.

     The source of the funds for all transactions referred to herein is working
capital and common stock of E&S.

ITEM 4.   PURPOSE OF TRANSACTION.

     On April 22, 1998, E&S, E&S Merger Corp., a wholly owned subsidiary of E&S
(the "Merger Sub"), and the Issuer entered into the Agreement and Plan of
Merger, dated April 22, 1998 (the "Merger Agreement"), which provides that the
Issuer will be merged (the "Merger") with and into Merger Sub on the terms and
subject to the conditions set forth
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 4 of 10 Pages
________________________________________________________________________________

in the Merger Agreement, with Merger Sub continuing as the surviving corporation
(the "Surviving Corporation"). E&S requested the Stockholders to enter into the
Voting Agreement as an inducement to E&S to execute the Merger Agreement. The
Voting Agreement described herein is intended to provide greater certainty that
E&S's acquisition of Issuer will be consummated.

     If the Merger is consummated in accordance with the terms of the Merger
Agreement, the Board of Directors of the Surviving Corporation shall initially
consist of three (3) members, all of whom shall be officers or employees of E&S.
Additionally, the Common Stock of the Issuer will cease to be quoted on the
NASDAQ system.

     Other than described above, E&S has no plans or proposals which related to,
or may result in, any of the matters listed in Items 4(a) - (j) of Schedule 13D
(although E&S reserves the right to develop such plans).


ITEM 5.   INTEREST IN SECURITIES OF THE ISSUER.

     As a result of the Voting Agreement, E&S may be deemed to have beneficial
ownership of 3,159,963 shares of Common Stock for purposes of Rule 14d-1 (a)
promulgated under the Securities Act of 1934, as amended, which represents
approximately 37% of the shares of Common Stock outstanding (based on the number
of shares of Common Stock outstanding on March 2, 1998, as represented to E&S by
the Issuer in the Merger Agreement).

     To the best of E&S's knowledge, neither E&S nor any other person referred
to in Schedule A attached hereto beneficially owns or has acquired or disposed
of any shares of Common Stock of the Issuer during the past 60 days.


ITEM 6.   CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
          TO SECURITIES OF THE ISSUER.

     The Stockholders entered into the Voting Agreement as an inducement to E&S
to enter into the Merger Agreement. Pursuant to the Merger Agreement and subject
to the terms and conditions set forth therein (including approval by the holders
of the Issuer's outstanding shares of Common Stock and expiration or termination
of the waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of
1976, as amended), the Issuer will merge with and into Merger Sub, with Merger
Sub continuing as the Surviving Corporation, and each issued and outstanding
share of Common Stock will be converted into the right to receive a number of
shares of E&S Common Stock having a value equal to $5.75 or, at the option of
each Issuer stock holder, $5.75 in cash.  The amount of cash payable by E&S to
the Issuer's stockholders in connection with the acquisition of their shares
will be limited to 48% of the aggregate consideration paid by E&S in order to
preserve the treatment of the Merger as a tax-free reorganization for federal
income tax purposes.  No monetary consideration was paid by E&S to the
Stockholders for the Voting Agreement.

     Pursuant to the Voting Agreement, the Stockholders have agreed to vote
their shares of Common Stock (i) in favor of the Merger, (ii) against any action
that would constitute a breach of the Merger Agreement or the Voting Agreement
and (iii) against any action that could interfere with the transactions
contemplated by the Merger Agreement, including, without limitation, any
competing business combination, all as more fully described in, and under the
circumstances set forth in, the Voting Agreement; provided, however, that the
Stockholders are not required to vote in favor of the Merger if the Board of
Directors of the Issuer has determined that the Issuer has received a Superior
Proposal (as such term is defined in the Merger Agreement) from a third party.
In addition, pursuant to the Voting Agreement, each of the 
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 5 of 10 Pages
________________________________________________________________________________


Stockholders has granted E&S an irrevocable proxy to vote their respective
shares of Common Stock if they fail to comply with their obligation to vote
their shares of Common Stock in the manner required by the Voting Agreement.

     The descriptions herein of the Voting Agreement and the Merger Agreement
are qualified in their entirety by reference to such agreements, copies of which
are filed hereto as Exhibits 2.1 and 99.1, and which are specifically
incorporated herein by reference in their entirety.

     Except as provided in the Merger Agreement and the Voting Agreement, none
of the persons named in Item 2 has any contracts, arrangements, understandings
or relationships (legal or otherwise) with any persons with respect to any
securities of the Issuer, including, but not limited to, transfers or voting of
any securities, finder's fees, joint ventures, loan or option arrangements, puts
or calls, guarantees of profits, division of profits or loss, or the giving or
withholding of proxies.


ITEM 7.   MATERIAL TO BE FILED AS EXHIBITS.

     Exhibit        Description
     -------        -----------

     2.1       Agreement and Plan of Merger, dated April 22, 1998, among E&S,
               Merger Sub and the Issuer.

     99.1      Voting Agreement, dated April 22, 1998, among E&S, Stephen L.
               Bartlett, Nancy E. Bush, Jeffrey W. Dunn, Lew S. Epstein, David
               W. Pidwell, Niraj Swarup, Arthur Yan, Advanced Technology
               Ventures IV, L.P., STF II, L.P., Asset Management Associates
               1996, L.P., AVI Capital, L.P., Associated Venture Investors II,
               L.P., AVI Partners Growth Fund II, L.P., and AVI Silicon Valley
               Partners, L.P.
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 6 of 10 Pages
________________________________________________________________________________

                                   SIGNATURE

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this Schedule 13D is true, complete
and accurate.


May 1, 1998                              EVANS & SUTHERLAND COMPUTER CORPORATION



                              By: /S/ Mark C. McBride
                                 -----------------------------------------------
                              Name: Mark C. McBride
                              Title: Vice President, Corporate Controller and
                                     Corporate Secretary
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 7 of 10 Pages
________________________________________________________________________________



                                 EXHIBIT INDEX
                                 -------------


     Exhibit   Description
     -------   -----------

     2.1       Agreement and Plan of Merger, dated April 22, 1998, among E&S,
               Merger Sub and the Issuer.

    99.1       Voting Agreement, dated April 22, 1998, among E&S, Stephen L.
               Bartlett, Nancy E. Bush, Jeffrey W. Dunn, Lew S. Epstein, David
               W. Pidwell, Niraj Swarup, Arthur Yan, Advanced Technology
               Ventures IV, L.P., STF II, L.P., Asset Management Associates
               1996, L.P., AVI Capital, L.P., Associated Venture Investors II,
               L.P., AVI Partners Growth Fund II, L.P., and AVI Silicon Valley
               Partners, L.P.
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 8 of 10 Pages
________________________________________________________________________________



                                  SCHEDULE A

  Directors and Executive Officers of Evans & Sutherland Computer Corporation
  ---------------------------------------------------------------------------

I.   Directors

<TABLE> 
<CAPTION> 
                                   Present Principal Occupation
Name                                  and Business Address                      Citizenship
-------------------------          ----------------------------                 -----------
<S>                                <C>                                          <C>
Stewart Carrell                    Chairman of the Board and Director           United States
                                     of Evans & Sutherland Computer
                                     Corporation
                                   600 Komas Drive
                                   Salt Lake City, Utah 84108


Gerald S. Casilli                  Chairman of the Board of                     United States
                                     Ikos Systems, Inc.
                                   19050 Prune Ridge Ave.
                                   Cupertino, California 95014


Peter O. Crisp                     General Partner of Venrock                   United States
                                     Associates
                                   Room 5600
                                   30 Rockefeller Plaza
                                   New York, New York 10112


James R. Oyler                     Director; President and                      United States
                                     Chief Executive Officer of
                                     Evans & Sutherland Computer
                                     Corporation
                                   600 Komas Drive
                                   Salt Lake City, Utah 84108

</TABLE> 
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                        Page 9 of 10 Pages
________________________________________________________________________________

<TABLE> 
<S>                                <C>                                          <C>
Ivan E. Sutherland                 Vice President and Fellow for                United States
                                     Sun Microsystems, Inc.
                                   2600 Casey Ave.
                                   Building 29
                                   Mountain View, California 94043


 John E. Warnock                   Chairman and Chief Executive                 United States
                                     Officer of Adobe Systems, Inc.
                                   345 Park Ave.
                                   San Jose, California 95110
</TABLE> 

II.  Executive Officers

<TABLE> 
<CAPTION> 
                                   Present Principal Occupation
Name                                   and Business Address                     Citizenship
-------------------------          ----------------------------                 -----------
<S>                                <C>                                          <C>
Ronald R. Sutherland               Vice President and General                   United States
                                     Manager of Government
                                     Simulation
                                   600 Komas Drive
                                   Salt Lake City, Utah 84108


John T. Lemley                     Vice President and Chief                     United States
                                     Financial Officer
                                   600 Komas Drive
                                   Salt Lake City, Utah 84108


Charles R. Maule                   Vice President and General                   United States
                                     Manager of Desktop Graphics
                                   600 Komas Drive
                                   Salt Lake City, Utah 84108
</TABLE> 
<PAGE>
 
________________________________________________________________________________
CUSIP No.  00430P 10 4                                       Page 10 of 10 Pages
________________________________________________________________________________

<TABLE> 
<S>                                <C>                                          <C>
Mark C. McBride                    Vice President, Corporate                    United States
                                     Controller and Corporate
                                     Secretary
                                   600 Komas Drive
                                   Salt Lake City, Utah 84108
</TABLE> 
