<PAGE>   1
                                                                   EXHIBIT 10.16


                                VOTING AGREEMENT


                  VOTING AGREEMENT (this "Agreement"), dated as of February 18,
1999, is entered into by and among DIAGNOSTIC HEALTH SERVICES, INC., a Delaware
corporation ("DHS"), MAI ACQUISITION CORP., a Texas corporation ("Merger
Subsidiary"), those stockholders of DHS whose signatures appear on the
signature pages hereof (each a "DHS Holder" and collectively the "DHS
Holders"), and those shareholders of MEDICAL ALLIANCE, Inc., a Texas
corporation ("MAI"), whose signatures appear on the signature pages hereof
(each a "MAI Holder" and collectively the "MAI Holders");


                             W I T N E S S E T H :

                  WHEREAS, contemporaneous with the execution and delivery of
this Agreement, DHS, Merger Subsidiary and MAI have entered into an Agreement
and Plan of Merger of even date herewith (the "Merger Agreement"; all
capitalized terms used herein without definition having the respective meanings
ascribed to them in the Merger Agreement); and

                  WHEREAS, as a condition and inducement to DHS and Merger
Subsidiary entering into the Merger Agreement and incurring the obligations set
forth therein and the DHS Holders entering into this Agreement and incurring
the obligations set forth herein, the MAI Holders have agreed to vote and to
cause to be voted all of the shares of common stock of MAI, $.002 par value per
share (the "MAI Common Stock"), now owned or hereafter acquired by them, for
and in favor of the merger of Merger Subsidiary with and into MAI (the
"Merger") and (to the extent they are entitled to vote thereon) the Name
Change, and the other transactions provided for in the Merger Agreement; and

                  WHEREAS, as a condition and inducement to the MAI Holders
entering into this Agreement and incurring the obligations set forth herein,
the DHS Holders have agreed to vote and to cause to be voted all of the shares
of common stock of DHS, $.001 par value per share (the "DHS Common Stock"), now
owned or hereafter acquired by them, for and in favor of (a) the issuance of
DHS Common Stock in the Merger, and (b) the Name Change;

                  NOW, THEREFORE, in consideration of the premises and the
respective covenants and agreements set forth herein and in the Merger
Agreement, the parties hereto, intending to be legally bound hereby, agree as
follows:

                  SECTION 1. VOTING OF MAI COMMON STOCK. Each of the MAI
Holders hereby agrees that, during the period commencing on the date hereof and
continuing until the first to occur of (a) the Effective Time of the Merger, or
(b) the termination of this Agreement in accordance with its terms, (i) such
MAI Holder will not sell or transfer any MAI Common Stock now owned or
hereafter acquired by such MAI Holder (the "MAI Shares") or any interest
therein to any person, other than an Affiliate of such MAI Holder who shall
agree to be bound by the terms of this Agreement to the same extent as such MAI
Holder, and (ii) at any meeting (whether annual or special and whether or not
an adjourned or postponed meeting) of the holders of MAI 


<PAGE>   2



Common Stock, however called, or in connection with any written consent of the
holders of MAI Common Stock, such MAI Holder will appear at the meeting or
otherwise cause the MAI Shares to be counted as present thereat for purposes of
establishing a quorum and vote or consent (or cause to be voted or consented)
the MAI Shares (A) in favor of the adoption of the Merger Agreement and the
approval of all other actions contemplated by the Merger Agreement and this
Agreement and any actions required in furtherance thereof and hereof, and (B)
against any action or agreement that would result in a breach in any respect of
any covenant, representation or warranty or any other obligation or agreement
of MAI under the Merger Agreement. Each MAI Holder further agrees not to enter
into any agreement or understanding with any Person the effect of which would
be inconsistent with or violative of any provision contained in this Section 1.

                  SECTION 2. VOTING OF DHS COMMON STOCK. Each DHS Holder hereby
agrees that, during the period commencing on the date hereof and continuing
until the first to occur of (a) the Effective Time of the Merger, or (b) the
termination of this Agreement in accordance with its terms, (i) such DHS Holder
will not sell or transfer any DHS Common Stock now owned or hereafter acquired
by such DHS Holder (the "DHS Shares") or any interest therein to any person,
other than an Affiliate of such DHS Holder who shall agree to be bound by the
terms of this Agreement to the same extent as such DHS Holder, and (ii) at any
meeting (whether annual or special and whether or not an adjourned or postponed
meeting) of the holders of DHS Common Stock, however called, or in connection
with any written consent of the holders of DHS Common Stock, such DHS Holder
will appear at the meeting or otherwise cause the DHS Shares to be counted as
present thereat for purposes of establishing a quorum and vote or consent (or
cause to be voted or consented) the DHS Shares (A) in favor of the issuance of
DHS Common Stock in the Merger and any actions required in furtherance thereof
or in furtherance of the Merger, (B) in favor of the Name Change, and (C)
against any action or agreement that would result in a breach in any respect of
any covenant, representation or warranty or any other obligation or agreement
of DHS under the Merger Agreement. Each DHS Holder hereby further agrees not to
enter into any agreement or understanding with any Person the effect of which
would be inconsistent with or violative of any provision contained in this
Section 2.

                  SECTION 3. COVENANTS, REPRESENTATIONS AND WARRANTIES OF MAI
HOLDERS. Each MAI Holder (severally, and not jointly and severally) hereby
represents and warrants to, and agrees with, DHS as follows:

                  (a) Ownership of Shares. Such MAI Holder is the sole record
and beneficial owner of that number of shares of MAI Common Stock set forth
next to such MAI Holder's name on Schedule 1 annexed hereto. On the date
hereof, such MAI Shares constitute all of the shares of MAI Common Stock owned
of record or beneficially owned by such MAI Holder. Such MAI Holder has sole
voting power and sole power to issue instructions with respect to the matters
set forth in Section 1 hereof, sole power of disposition, and sole power to
agree to all of the matters set forth in this Agreement, in each case with
respect to all of such MAI Shares with no limitations, qualifications or
restrictions on such rights, subject to applicable securities laws and the
terms of this Agreement.


                                       2

<PAGE>   3

                  (b) Authorization. This Agreement has been duly and validly
executed and delivered by such MAI Holder and constitutes a valid and binding
agreement enforceable against such MAI Holder in accordance with its terms
except (i) as may be limited by applicable bankruptcy, insolvency or similar
laws affecting creditors' rights, and (ii) that the remedy of specific
performance and injunctive and other forms of equitable relief may be subject
to equitable defenses and to the discretion of the court before which any
proceeding therefor may be brought.

                  (c) No Conflicts. Except for filings, authorizations,
consents and approvals as may be required under the HSR Act, the 1933 Act and
the 1934 Act, (i) no filing with, and no permit, authorization, consent or
approval of, any state or federal Governmental Authority is necessary for the
execution of this Agreement by such MAI Holder and the consummation by such MAI
Holder of the transactions contemplated hereby, and (ii) none of the execution
and delivery of this Agreement by such MAI Holder, the consummation by such MAI
Holder of the transactions contemplated hereby or compliance by such MAI Holder
with any of the provisions hereof will (A) conflict with or result in any
breach of the organizational documents of such MAI Holder, (B) result in a
violation or breach of, or constitute (with or without notice or lapse of time
or both) a default (or give rise to any third party right of termination,
cancellation, material modification or acceleration) under any of the terms,
conditions or provisions of any note, loan agreement, bond, mortgage,
indenture, license, contract, commitment, arrangement, understanding, agreement
or other instrument or obligation of any kind to which such MAI Holder is a
party or by which such MAI Holder or any of its properties or assets may be
bound, or (C) violate any order, writ, injunction, decree, judgment, statute,
rule or regulation applicable to such MAI Holder or any of his or its
properties or assets.

                  (d) No Encumbrances. Except as applicable in connection with
the transactions contemplated by Section 1 hereof, the MAI Shares, at all times
during the term hereof, will be beneficially owned by such MAI Holder and
Affiliates thereof referred to in Section 1 of this Agreement, free and clear
of all proxies or voting trusts or other such agreements, except for any such
matters arising hereunder.

                  (e) Restriction on Transfer, Proxies and Non-Interference.
Such MAI Holder will not, directly or indirectly, from the date hereof through
the termination of this Agreement, (i) except as permitted by Section l above,
offer for sale, sell, transfer, tender, pledge, encumber, assign or otherwise
dispose of, or enter into any contract, option or other arrangement or
understanding with respect to or consent to the offer for sale, sale, transfer,
tender, pledge, encumbrance, assignment or other disposition of, any or all of
the MAI Shares or any interest therein; (ii) grant any proxies or powers or
attorney, deposit the MAI Shares into a voting trust or enter into a voting
agreement with respect to the MAI Shares (other than this Agreement); or (iii)
take any action that would make any representation or warranty of such MAI
Holder contained herein untrue or incorrect or would result in a breach by such
MAI Holder of its obligations under this Agreement.





                                       3
<PAGE>   4


                  SECTION 4. COVENANTS, REPRESENTATIONS AND WARRANTIES OF DHS
HOLDERS. Each DHS Holder (severally, and not jointly and severally) hereby
represents and warrants to, and agrees with, the MAI Holders as follows:

                  (a) Ownership of Shares. Such DHS Holder is the sole record
and beneficial owner of that number of shares of DHS Common Stock set forth
next to such DHS Holder's name on Schedule 1 annexed hereto. On the date
hereof, such DHS Shares constitute all of the shares of DHS Common Stock owned
of record or beneficially owned by such DHS Holder. Such DHS Holder has sole
voting power and sole power to issue instructions with respect to the matters
set forth in Section 2 hereof, sole power of disposition, and sole power to
agree to all of the matters set forth in this Agreement, in each case with
respect to all of such DHS Shares with no limitations, qualifications or
restrictions on such rights, subject to applicable securities laws and the
terms of this Agreement.

                  (b) Corporate Authorization. This Agreement has been duly and
validly executed and delivered by such DHS Holder and constitutes a valid and
binding agreement enforceable against such DHS Holder in accordance with its
terms except (i) as may be limited by applicable bankruptcy, insolvency or
similar laws affecting creditors' rights, and (ii) that the remedy of specific
performance and injunctive and other forms of equitable relief may be subject
to equitable defenses and to the discretion of the court before which any
proceeding therefor may be brought.

                  (c) No Conflicts. Except for filings, authorizations,
consents and approvals as may be required under the HSR Act, the 1933 Act and
the 1934 Act, (i) no filing with, and no permit, authorization, consent or
approval of, any state or federal Governmental Authority is necessary for the
execution of this Agreement by such DHS Holder and the consummation by such DHS
Holder of the transactions contemplated hereby, and (ii) none of the execution
and delivery of this Agreement by such DHS Holder, the consummation by such DHS
Holder of the transactions contemplated hereby or compliance by such DHS Holder
with any of the provisions hereof will (A) conflict with or result in any
breach of the organizational documents of such DHS Holder, (B) result in a
violation or breach of, or constitute (with or without notice or lapse of time
or both) a default (or give rise to any third party right of termination,
cancellation, material modification or acceleration) under any of the terms,
conditions or provisions of any note, loan agreement, bond, mortgage,
indenture, license, contract, commitment, arrangement, understanding, agreement
or other instrument or obligation of any kind to which such DHS Holder is a
party or by which such DHS Holder or any of its properties or assets may be
bound, or (C) violate any order, writ, injunction, decree, judgment, statute,
rule or regulation applicable to such DHS Holder or any of its properties or
assets.

                  (d) No Encumbrances. Except as applicable in connection with
the transactions contemplated by Section 2 hereof, the DHS Shares, at all times
during the term hereof, will be beneficially owned by such DHS Holder and
Affiliates thereof referred to in Section 2 of this Agreement, free and clear
of all liens, claims, security interests, proxies, voting trusts or agreements,
understandings or arrangements or any other encumbrances whatsoever, except for
any such matters arising hereunder.




                                       4
<PAGE>   5



                  (e) No Finder's Fees. Except as set forth in the Merger
Agreement, no broker, investment banker, financial advisor or other person is
entitled to any broker's, finder's, financial adviser's or other similar fee or
commission in connection with the transactions contemplated by this Agreement
based upon arrangements made by or on behalf of such DHS Holder.

                  (f) Restriction on Transfer, Proxies and Non-Interference.
Such DHS Holder will not, directly or indirectly, at any time prior to the
termination of this Agreement, (i) except as permitted by Section 2(i) above,
offer for sale, sell, transfer, tender, pledge, encumber, assign or otherwise
dispose of, or enter into any contract, option or other arrangement or
understanding with respect to or consent to the offer for sale, sale, transfer,
tender, pledge, encumbrance, assignment or other disposition of, any or all of
the DHS Shares or any interest therein; (ii) grant any proxies or powers of
attorney, deposit the DHS Shares into a voting trust or enter into a voting
agreement with respect to the DHS Shares (other than this Agreement); or (iii)
take any action that would make any representation or warranty of such DHS
Holder contained herein untrue or incorrect or would result in a breach by such
DHS Holder of his, her or its obligations under this Agreement.

                  SECTION 5. REPRESENTATIONS AND WARRANTIES OF DHS. DHS hereby
represents and warrants to the MAI Holders as follows:

                  (a) Organization. DHS is a corporation duly organized,
validly existing and in good standing under the laws of the State of Delaware
and has all requisite corporate power and authority to execute and deliver this
Agreement and perform its obligations hereunder. The execution and delivery by
DHS of this Agreement and the performance by DHS of its obligations hereunder
have been duly and validly authorized by the Board of Directors of DHS and no
other corporate proceedings on the part of DHS are necessary to authorize the
execution, delivery or performance of this Agreement or the consummation of the
transactions contemplated hereby by DHS.

                  (b) Corporate Authorization. This Agreement has been duly and
validly executed and delivered by DHS and constitutes a valid and binding
agreement of DHS enforceable against DHS in accordance with its terms, except
(i) as may be limited by applicable bankruptcy, insolvency or similar laws
affecting creditors' rights, and (ii) that the remedy of specific performance
and injunctive and other forms of equitable relief may be subject to equitable
defenses and to the discretion of the court before which any proceeding
therefor may be brought.

                  (c) No Conflicts. Except for filings, authorizations,
consents and approvals as may be required under the HSR Act, the 1933 Act and
the 1934 Act, (i) no filing with, and no permit, authorization, consent or
approval of, any state or federal Governmental Authority is necessary for the
execution of this Agreement by DHS and the consummation by DHS of the
transactions contemplated hereby, and (ii) none of the execution and delivery
of this Agreement by DHS, the consummation by DHS of the transactions
contemplated hereby, or compliance by DHS with any of the provisions hereof
will (A) conflict with or result in any breach of the certificate of
incorporation or by-laws of DHS, (B) result in a violation or breach of, or
constitute 




                                       5
<PAGE>   6


(with or without notice or lapse of time or both) a default (or give rise to
any third party right of termination, cancellation, material modification or
acceleration) under any of the terms, conditions or provisions of any note,
loan agreement, bond, mortgage, indenture, license, contract, commitment,
arrangement, understanding, agreement or other instrument or obligation of any
kind to which DHS is a party or by which DHS or any of its properties or assets
may be bound, or (C) violate any order, writ, injunction, decree, judgment,
statute, rule or regulation applicable to DHS or any of its properties or
assets.

                  SECTION 6. TERMINATION. This Agreement will terminate upon
the earlier of (i) the consummation of the Merger, or (ii) the termination of
the Merger Agreement in accordance with its terms.

                  SECTION 7. MISCELLANEOUS.

                  (a) Entire Agreement. This Agreement constitutes the entire
agreement among the parties with respect to the subject matter hereof and
supersedes all other prior agreements and understandings, both written and
oral, between the parties with respect to the subject matter hereof.

                  (b) Assignments: Rights of Assignees: Third Party
Beneficiaries. This Agreement shall not be assignable by any party hereto
without the consent of the other parties. This Agreement shall be binding upon,
inure to the benefit of, and be enforceable by, the parties hereto and their
respective heirs, executors, administrators, legal representatives, successors
and permitted assigns. Nothing expressed or referred to in this Agreement is
intended or shall be construed to give any person other than the parties to
this Agreement or their respective heirs, executors, administrators, legal
representatives, successors or permitted assigns any legal or equitable right,
remedy or claim under or in respect of this Agreement or any provision
contained herein.

                  (c) Specific Performance. The parties hereto acknowledge that
money damages are an inadequate remedy for breach of this Agreement because of
the difficulty of ascertaining the amount of damage that will be suffered by
the non-breaching party or parties in the event that this Agreement is
breached. Therefore, each of the parties agrees that the non-breaching party or
parties may obtain specific performance of this Agreement and injunctive relief
against any breach hereof without the necessity of establishing irreparable
harm.

                  (d) Waiver. No waiver of any provision of this Agreement
shall be effective unless it is in writing signed by the party granting the
waiver, and a waiver by any party hereto of any one or more defaults shall not
operate as a waiver of any future default or defaults, whether of a like or of
a different character. No waiver of any of the provisions of this Agreement
shall constitute a waiver of any other provisions (whether or not similar), nor
shall such a waiver constitute a continuing waiver, unless otherwise expressly
provided.

                  (e) Section Headings. Headings contained in this Agreement
are inserted only as a matter of convenience and in no way define, limit, or
extend the scope or intent of this Agreement or any provisions thereof.





                                       6
<PAGE>   7



                  (f) Choice of Law. This Agreement will be governed by and
construed and enforced in accordance with the laws of the State of Texas
(without regard to the principles of conflicts of law) applicable to a contract
executed and to be performed in such State. Each party hereto (i) agrees to
submit to personal jurisdiction and to waive any objection as to venue in the
state or federal courts located in Dallas County, Texas, (ii) agrees that any
action or proceeding shall be brought exclusively in such courts, unless
subject matter jurisdiction or personal jurisdiction cannot be obtained, and
(iii) agrees that service of process on any party in any such action shall be
effective if made by registered or certified mail addressed to such party at
the address specified herein, or to any parties hereto at such other addresses
as he, she or it may from time to time specify to the other parties in writing
for such purpose. The exclusive choice of forum set forth in this Section 7(g)
shall not be deemed to preclude the enforcement of any judgment obtained in
such forum or the taking of any action under this Agreement to enforce such
judgment in any appropriate jurisdiction.

                  (g) Notices. All notices, requests and other communications
to any party hereunder shall be in writing and will be deemed to have been duly
given only if delivered personally or by facsimile transmission or mailed
(first class mail postage prepaid), or by overnight express courier (charges
prepaid or billed to the account of the sender) to the parties at the following
addresses or facsimile numbers:

               If to DHS, to:            Diagnostic Health Services, Inc.
                                         2777 Stemmons Freeway
                                         Suite 1525
                                         Dallas, Texas  75207
                                         Fax:  (214) 631-8537
                                         Attention:  Brad A. Hummel

               If to any of the of
                 MAI Holders or
                 DHS Holders:            At his, her or its address set forth
                                         on Schedule 1 annexed hereto

               with a copy to
                in each case to:         Greenberg Traurig
                                         200 Park Avenue
                                         New York, New York  10166
                                         Fax:  (212) 801-6400
                                         Attention:  Shahe Sinanian, Esq.

                                                     - and -

                                         Jackson Walker L.L.P.
                                         901 Main Street, Suite 6000
                                         Dallas, Texas  75202
                                         Fax:  (214) 953-5822
                                         Attention:  Richard F. Dahlson, Esq.




                                       7
<PAGE>   8


or to such other address or fax number as any party may have furnished to the
others in writing in accordance herewith.

                  (h) Counterparts. This Agreement may be executed in any
number of counterparts, each of which shall be deemed to be an original, but
all of which together shall constitute one and the same document.

                  (i) Severability of Provisions. If any term, provision,
covenant or restriction of this Agreement is held by a court of competent
jurisdiction to be invalid, void or unenforceable, the remainder of the terms,
provisions, covenants and restrictions of this Agreement shall remain in full
force and effect and shall not in any way be affected, impaired or invalidated.

                  SECTION 8. EFFECTIVENESS. This Agreement shall become
effective simultaneously with the execution and delivery of the Merger
Agreement.

                  SECTION 9. THE INDIVIDUAL STOCKHOLDERS. The individuals
executing this Agreement are executing this Agreement solely so that this
Agreement will constitute a "stockholders' agreement" within the meaning of
Section 218(c) of the Delaware General Corporation Law and will not have any
rights or obligations hereunder except to vote in accordance with Section 1 and
Section 2, as applicable.

              [THE REMAINDER OF THIS PAGE IS INTENTIONALLY BLANK]




                                       8
<PAGE>   9




                  IN WITNESS WHEREOF, the parties hereto have caused this
Agreement to be duly executed as of the date first set forth above.

                          DIAGNOSTIC HEALTH SERVICES, INC.

                          By: /s/ BRAD HUMMEL
                             -----------------------------------


                          MAI ACQUISITION CORP.

                          By: /s/ BRAD HUMMEL
                             -----------------------------------


                          MAI Holders:

                          MAPLELEAF CAPITAL, LTD.

                          By: /s/ JIM SILCOCK
                             -----------------------------------


                          SUNWESTERN CAYMAN 1998 PARTNERS

                          By: /s/ JIM SILCOCK
                             -----------------------------------


                          SUNWESTERN INVESTMENT FUND III

                          By: /s/ JIM SILCOCK
                          --------------------------------------

                              /s/ PAUL R. HERCHMAN
                          --------------------------------------
                                     Paul R. Herchman
   
                              /s/ GARY B. HILL
                          --------------------------------------
                                       Gary B. Hill

                              /s/ DAVID A. KALLENBERGER
                          --------------------------------------
                                   David A. Kallenberger

                              /s/ THOMAS A. MONTGOMERY
                          --------------------------------------
                                    Thomas A. Montgomery





                                       9
<PAGE>   10



                              /s/ LEON PRITZKER
                             -----------------------------------
                                        Leon Pritzker


                              /s/ TONY LEVECCHIO
                             -----------------------------------
                                        Tony LeVecchio

                             DHS Holders:

                              /s/ MAX W. BATZER
                             -----------------------------------
                                         Max W. Batzer

                              /s/ BRAD A. HUMMEL
                             -----------------------------------
                                        Brad A. Hummel

                              /s/ JAMES R. ANGELICA
                             -----------------------------------
                                      James R. Angelica

                              /s/ THOMAS M. SESTAK
                             -----------------------------------
                                       Thomas M. Sestak

                              /s/ BO W. LYCKE
                             -----------------------------------
                                         Bo W. Lycke

                              /s/ BONNIE G. LANKFORD
                             -----------------------------------
                                      Bonnie G. Lankford





                                      10
<PAGE>   11






                         Schedule 1 to Voting Agreement
                         ------------------------------

<TABLE>
<CAPTION>

MAI Holders                                                                                           MAI Shares
-----------                                                                                           ----------

<S>                                                                                                   <C>    
Mapleleaf Capital, Ltd.                                                                                 738,330

Sunwestern Cayman 1998 Partners                                                                         135,649

Sunwestern Investment Fund III                                                                          125,214

Paul R. Herchman                                                                                        470,646

Gary B. Hill                                                                                              5,000

David A. Kallenberger                                                                                   167,027

Thomas A. Montgomery                                                                                    187,711

Leon Pritzker                                                                                            80,454

Tony LeVecchio                                                                                           18,815
</TABLE>







<PAGE>   12




<TABLE>
<CAPTION>
DHS Holders                                                                                           DHS Shares
-----------                                                                                           ----------

<S>                                                                                                  <C>    
Max W. Batzer                                                                                           154,750
c/o Diagnostic Health Services, Inc.
2777 Stemmons Freeway, Suite 1525
Dallas, TX  75207

Brad A. Hummel                                                                                            8,593
c/o Diagnostic Health Services, Inc.
2777 Stemmons Freeway, Suite 1525
Dallas, TX  75207

James R. Angelica                                                                                       315,052
Diagnostic Health Services, Inc.
9717 Landmark Parkway Drive
Suite 102
St. Louis, MO  63127

Thomas M. Sestak                                                                                        126,421
Standard Construction of San Francisco
1226 Ninth Avenue
San Francisco, CA  94122

Bo W. Lycke                                                                                               1,000
ClaimsNet.Com
12801 North Central Expressway
Suite 1515
Dallas, TX  75243

Bonnie G. Lankford                                                                                       32,911
c/o Diagnostic Health Services, Inc.
2777 Stemmons Freeway, Suite 1525
Dallas, TX  75207
</TABLE>