<PAGE>   1
                                                                   EXHIBIT 10.51


                                                [OFFICERS/EMPLOYEES/CONSULTANTS]

                             RENAL CARE GROUP, INC.

                      NON-QUALIFIED STOCK OPTION AGREEMENT
                                   (1999 PLAN)

                                  RONALD HINDS

         THIS AGREEMENT is made as of the Date of Grant, by RENAL CARE GROUP,
INC., a corporation organized and existing under the laws of the State of
Delaware (the "Company"), to RONALD HINDS (the "Optionee").

         Upon and subject to the Additional Terms and Conditions attached hereto
and incorporated herein by reference as part of this Agreement, the Company
hereby awards as of the Date of Grant to Optionee an option (the "Option"), as
described below, to purchase the Option Shares.

         A.       DATE OF GRANT:    August 30, 1999.

         B.       TYPE OF OPTION:   Non-Qualified Stock Option.

         C.       EXERCISE PRICE PER SHARE: $18.25.

         D.       OPTION SHARES:    140,000 shares of the Company's Common
                                    Stock, $.01 par value.

         E.       VESTING SCHEDULE:

                  The Vesting Schedule shall be as follows:

 <TABLE>
<CAPTION>
                                                                      Percentage of Option
                           Schedule                                       Shares Vested
                           --------                                       -------------
<S>                                                                   <C>
                  Date of Grant                                                 20%

                  1st anniversary of                                            40%
                  the Date of Grant

                  2nd anniversary of                                            60%
                  the Date of Grant

                  3rd anniversary of                                            80%
                  the Date of Grant

                  4th anniversary of                                            100%
                  the Date of Grant
</TABLE>


<PAGE>   2


                                                [OFFICERS/EMPLOYEES/CONSULTANTS]


         F.       EXPIRATION DATE: This Option may be exercised at any time
                  after the Date of Grant through 5:00 p.m., Nashville,
                  Tennessee time, on the10th anniversary of the Date of Grant,
                  provided that this Option may be exercised as to no more than
                  the vested Option Shares, determined pursuant to the Vesting
                  Schedule or as modified as provided herein.

         IN WITNESS WHEREOF, the Company has executed this Agreement the 30th
day of August, 1999.

                                            RENAL CARE GROUP, INC.



                                            By: /s/ Sam A. Brooks
                                                --------------------------------
                                                Sam A. Brooks, President

ATTEST:


/s/ Douglas B. Chappell
--------------------------------------
Douglas B. Chappell, Secretary

                                            OPTIONEE:



                                            /s/ Ronald Hinds
                                            ------------------------------------
                                            Ronald Hinds

WITNESS:




---------------------------


                                       2
<PAGE>   3

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]



                         ADDITIONAL TERMS AND CONDITIONS
                             RENAL CARE GROUP, INC.
                      NON-QUALIFIED STOCK OPTION AGREEMENT
                                FOR RONALD HINDS

         1. Exercise of Option. This Option may be exercised in whole or in
part, but in no less than one hundred (100) share lots, by written notice, in
substantially the form as Exhibit 1 hereto, directed to the Secretary of the
Company at its principal place of business, accompanied by payment of the
Exercise Price for the number of shares purchased. Payment shall be made in
cash, by check, or in shares of Common Stock already held by the Optionee prior
to the exercise of the Option. In the event that all or part of the Exercise
Price is paid in shares of Common Stock, the value of such shares shall be equal
to the Fair Market Value of such shares on the date of exercise of the Option,
and the Optionee shall deliver to the Company a certificate or certificates for
such shares.

         2. Issuance of Option Shares. Upon a valid exercise of this Option, the
Company shall, or shall direct its transfer agent to, make delivery of the
Option Shares as soon as reasonably possible; provided, however, that the
Company shall not be required to issue or deliver any certificates for Option
Shares pursuant to this Option prior to (a) the completion of any registration
or qualification of such shares under any federal or state law, or any ruling or
regulation of any governmental body which the Board shall, in its sole
discretion, determine to be necessary or advisable, and/or (b) the Optionee
making at the time of exercise any reasonable representations and warranties
requested by the Company in order to qualify the issuance of the Option Shares
for exemptions from registration under state or federal securities laws. The
Option Shares issued on the exercise of this Option, when paid for as herein
provided, will be fully paid and non-assessable.

         3. Termination of Employment or Death.

                  (a) In the event of a termination of Optionee's employment or
consulting services for any reason (other than a termination of an Optionee
employee by his or her death or disability), (i) except as provided in clause
(ii) of this sentence this Option shall terminate as of the day of notice of
such termination by either party, but in no event later than the Expiration
Date, and (ii) any unexercised portion of this Option which is otherwise
exercisable on the date of termination may be exercised by Optionee at any time
within three (3) months following the date of such termination, unless Optionee
dies during such three (3) month period, but in no event later than the
Expiration Date. If Optionee is an employee, whether military, government or
other service by Optionee or other leave of absence granted to Optionee shall
constitute such a termination shall be determined in each case by the Board



                                       3
<PAGE>   4

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]

at its discretion, and any determination by the Board shall be final and
conclusive. If the Board determines that such absence does not constitute such a
termination, however, Optionee may exercise his or her option only with the
consent of the Board.

                  (b) If Optionee is an employee, upon termination of Optionee's
employment with the Company (including its subsidiaries) as result of a
permanent disability (as defined by Section 22(e)(3) of the Code), (i) except as
provided in clause (ii) of this sentence, this Option shall terminate and be
unexercisable on the date of such termination, but in no event later than the
Expiration Date, and (ii) any unexercised portion of this Option which is
otherwise exercisable on the date of such termination may be exercised by
Optionee at any time within six (6) months following the date of such
termination, unless Optionee dies during such six (6) month period, but in no
event later than the Expiration Date.

                  (c) If Optionee is an employee, upon termination of his or her
employment by the Company without Cause, if there is a written employment
agreement between Optionee and the Company, this Option shall cease to vest in
accordance with the Vesting Schedule regardless of any salary continuation
specified by such employment agreement as a result of such termination. Upon
termination of his or her employment with the Company, (i) except as provided in
clause (ii) of this sentence, this Option shall terminate and be unexercisable
as to unvested options on the date of termination, but in no event later than
the Expiration Date, and (ii) any unexercised portion of this Option which is
otherwise exercisable as of such termination date may be exercised by Optionee
at any time within three (3) months following such termination date, unless
Optionee dies during such three (3) month period such option may be exercised
pursuant to subparagraph (d) below, but in no event later than the Expiration
Date. If there is no written employment agreement between Optionee and the
Company, upon termination of his or her employment by the Company without Cause
any unexercised portion of this Option shall terminate in accordance with
Section 3(a) above, but in no event later than the Expiration Date.

                  (d) If Optionee dies, (i) except as provided in clause (ii) of
this sentence, this Option shall terminate and be unexercisable on the date of
death, and (ii) any unexercised portion of this Option, if otherwise exercisable
at the date of death, may be exercised by his or her personal representatives,
heirs, or legatees at any time prior to the expiration of one (1) year after the
date of Optionee's death, but in no event later than the Expiration Date.

         4. Full Information. Optionee represents that he or she is familiar
with the business and affairs of the Company and realizes that the receipt of
the Option and Option Shares is a speculative investment and that any



                                       4
<PAGE>   5

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]

possible profit therefrom is uncertain. Optionee further represents that he or
she has had the opportunity to ask questions of and receive answers from the
Company and any person acting on its behalf and to obtain all information
available with respect to the Company and its affairs, and has received all
information and data with respect to the Company that he or she has requested
and which he or she has deemed relevant in connection with his or her receipt of
the Option and the Option Shares subject to the Option.

         5. No Rights in Option Stock. Optionee shall have no rights as a
stockholder with respect to any of the Option Shares prior to the date of
issuance to the Optionee of a certificate or certificates for such shares.
Optionee shall have no rights with respect to such shares not expressly
conferred by this Agreement.

         6. Stock Reserved. The Company shall at all times during the term of
this Agreement reserve and keep available such number of shares of the Common
Stock as will be sufficient to satisfy the requirements of this Agreement, and
shall pay all original issue taxes on the exercise of this Option, and all other
fees and expenses necessarily incurred by the Company in connection therewith.

         7. Nonassignability. This Option shall not be encumbered or transferred
in whole or in part except by will or the laws of descent and distribution and
is exercisable during the lifetime of the Optionee only by the Optionee.

         8. No Employment. This Agreement shall not give Optionee a right to
employment by, or membership on the board of directors of, the Company or its
subsidiaries.

         9. Non-Qualified Option. It is the intent of the parties hereto that
this Option be a non-qualified stock option and subject to all of the applicable
provisions of the Internal Revenue Code of 1986, as amended. The Company
recognizes that the Optionee may be subject to restrictions regarding his or her
right to trade Common Stock under applicable securities laws. Accordingly, the
Optionee may want to consider making an election to be taxed upon exercise of
this Option under Section 83(b) of the Code. The Optionee shall have sole
discretion to make such an election and shall be solely responsible for
complying with the Code and all relevant rules and regulations in connection
with such election. The Optionee shall provide written notice to the Company of
such election immediately after making such election.

         10. Share Adjustments. If the Company's outstanding shares of Common
Stock are increased or decreased or changed into or exchanged for a different
number or kind of shares or other securities of the Company by



                                       5
<PAGE>   6

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]

reason of any recapitalization, reclassification, stock split, combination of
shares, stock dividend, or transaction having similar effect, the Board shall
proportionately and appropriately adjust the number and kind of shares that are
subject to this Option and the Exercise Price Per Share, without any change in
the aggregate price to be paid therefor upon exercise of this Option.

         11. Changes in Control.

                  (a) Change in Control. Subject to Section 12, in the event
that a Change in Control shall occur, then (i) this Option (whether vested or
not vested) shall automatically become one hundred percent (100%) vested
immediately, and (ii) no other terms, conditions, restrictions or limitations
shall be imposed upon this Option after such date, and in no circumstance shall
this Option be forfeited on or after such date.

                  (b) Automatic Acceleration and Cash-Out. Subject to Section
12, upon a Change in Control that results directly or indirectly in the Common
Stock (or the stock of any successor the Company received in exchange for Common
Stock) ceasing to be publicly traded on a national securities market at any
time, (i) this Option shall automatically become one hundred percent (100%)
vested immediately with respect to the Option Shares, (ii) no other terms,
conditions, restrictions or limitations shall be imposed upon this Option after
such date, and in no circumstance shall this Option be forfeited on or after
such date, and (iii) this Option shall be valued and cashed out on the basis of
the Change in Control Price.

                  (c) Section 16 Insider. Notwithstanding anything herein to the
contrary, if the Optionee is subject to the reporting requirements of Section 16
of the Exchange Act with respect to the Company, and on the date of the Change
in Control this Option has not been outstanding for a period of at least six
months from the Date of Grant, the Optionee shall not be paid the consideration
described in this Section 11 above until the first day next following the end of
such six-month period.

         12. Modification, Extension and Renewal. The Board may modify, renew or
accept the surrender of this Option, including the acceleration or waiver of any
vesting or other restrictions or limitations, or the conversion of this Option
(with appropriate adjustments) to be applicable to the securities of any
successor corporation to the Company or parent of any such successor, and the
Board may authorize new options in substitution for the Option. Any substituted,
modified or converted options may bear such different or additional terms and
conditions as the Board shall deem appropriate. The determination of the Board
as to the terms of any of the foregoing may be made without regard to whether a
Change in Control has or has not occurred (or whether the Board has determined
that any event shall not be considered



                                       6
<PAGE>   7

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]

to be a Change in Control) and shall be conclusive and binding notwithstanding
the provisions hereof regarding exercisability. Any fractional shares resulting
from any of the foregoing adjustments under this Section shall be disregarded
and eliminated. However, no modification of this Option shall, without the
consent of the Optionee, adversely affect the rights or obligations of the
Optionee with respect to this Option.

         13. Administration. This Agreement shall be administered, construed and
interpreted by the Board.

         14. Definitions.

                  "Board" means the Board of Directors of the Company.

                  "Change in Control" means a change in control of the Company
of a nature that would be required to be reported (assuming such event has not
been "previously reported") in response to Item 1(a) of a Current Report on Form
8-K pursuant to Section 13 or 15(d) of the Exchange Act; provided that, without
limitation, a Change in Control shall also be deemed to have occurred at such
time as:

                  (i) any "person" within the meaning of Section 14(d) of the
         Exchange Act, other than the Company, a Subsidiary, or any employee
         benefit plan(s) sponsored by the Company or any Subsidiary, is or has
         become the "beneficial owner," as defined in Rule l3d-3 under the
         Exchange Act, directly or indirectly, of 25% or more of the combined
         voting power of the outstanding securities of the Company ordinarily
         having the right to vote at the election of directors;

                  (ii) individuals who constitute the Board immediately prior to
         any meeting of stockholders (the "Incumbent Board") have ceased for any
         reason to constitute at least a majority thereof after such shareholder
         meeting, provided that any person becoming a director whose election,
         or nomination for election by the Company's stockholders, was approved
         by a vote of at least three-quarters (3/4) of the directors comprising
         the Incumbent Board (either by a specific vote or by approval of the
         proxy statement of the Company in which such person is named as a
         nominee for director without objection to such nomination) shall be,
         for purposes of this Agreement, considered as though such person were a
         member of the Incumbent Board;

                  (iii) upon approval by the Company's stockholders of a
         reorganization, merger, share exchange or consolidation, other than one
         with respect to which those persons who were the beneficial owners,
         immediately prior to such reorganization, merger, share exchange or
         consolidation, of outstanding securities of the Company



                                       7
<PAGE>   8
                                                [OFFICERS/EMPLOYEES/CONSULTANTS]


         ordinarily having the right to vote in the election of directors own,
         immediately after such transaction, more than 75% of the outstanding
         securities of the resulting corporation ordinarily having the right to
         vote in the election of directors; or

                  (iv) upon approval by the Company's stockholders of a complete
         liquidation and dissolution of the Company or the sale or other
         disposition of all or substantially all of the assets of the Company
         other than to a Subsidiary.

                  Notwithstanding the occurrence of any of the foregoing, the
Board may determine, if it deems it to be in the best interest of the Company,
that an event or events otherwise constituting a Change in Control shall not be
so considered. Such determination shall be effective if it is made by the Board
prior to the occurrence of an event that otherwise would be or probably will
lead to a Change in Control or after such event if made by the Board a majority
of which is composed of directors who were members of the Board immediately
prior to the event that otherwise would be or probably will lead to a Change in
Control. Upon such determination, such event or events shall not be deemed to be
a Change in Control for any purposes hereunder, including but not limited to,
Section 12.

                  "Code" means the Internal Revenue Code of 1986, as amended.

                  "Common Stock" means the Common Stock, $.01 par value, of the
Company.

                  "Exchange Act" means the Securities Exchange Act of 1934, as
amended, and the rules and regulations thereunder.

                  "Fair Market Value" means the closing price of the shares of
Common Stock on a national securities exchange on the day on which such value is
to be determined or, if no shares were traded on such day, on the next preceding
day on which shares were traded, as reported by the National Quotation Bureau,
Inc. or other national quotation service. If the shares are not traded on an
exchange but are traded in the over-the-counter market, on the day on which such
value is to be determined or, if such "asked" price is not available, the last
sales price on such day or, if no shares were traded on such day, on the next
preceding day on which the shares were traded, as reported by the National
Association of Securities Dealers Automatic Quotation System (NASDAQ) or other
national quotation service.

                  "Subsidiary" means any corporation that qualifies as a
subsidiary of a corporation under the definition of "subsidiary corporation"
contained in Section 424(f) of the Code.



                                       8
<PAGE>   9

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]

                                    EXHIBIT 1


                              NOTICE OF EXERCISE OF
                            STOCK OPTION TO PURCHASE
                                 COMMON STOCK OF
                             RENAL CARE GROUP, INC.


                                      Name:
                                             -----------------------------------
                                      Address:
                                                --------------------------------
                                                --------------------------------

                                      Date:
                                            ------------------------------------

Renal Care Group, Inc.
Attention: [Secretary]
2100 West End, Suite 800
Nashville, Tennessee 37203

         Re: Exercise of Non-Qualified Stock Option

Ladies and Gentlemen:

         Subject to acceptance hereof in writing by Renal Care Group, Inc. (the
"Company"), I hereby give at least ten days but not more than thirty (30) days
prior notice of my election to exercise options granted to me to purchase
_____________ shares of Common Stock of the Company under the Renal Care Group,
Inc. Non-Qualified Stock Option Agreement granted on ______________________,
______. The purchase shall take place as of ______________________, ______ (the
"Exercise Date").

         On or before the Exercise Date, I will pay the applicable purchase
price by delivery of a certified check for $__________ for the full purchase
price payable to the order of Renal Care Group, Inc.

         The required federal, state and local income tax withholding, if any,
on the exercise of the option shall be paid on or before the Exercise Date.

         I hereby reaffirm that the representations made in Additional Terms and
Conditions of the Agreement are true and correct as of the date of exercising
this Option.



                                       9
<PAGE>   10

                                                [OFFICERS/EMPLOYEES/CONSULTANTS]


           As soon as the stock certificate is registered in my name, please
deliver it to me at the above address.

                                            Very truly yours,

AGREED TO AND ACCEPTED:



RENAL CARE GROUP, INC.



By:
   -----------------------------

Title:
      --------------------------

Number of Shares Exercised:
                           --------------
Number of Shares Remaining:
                           --------------
Date:
     -----------



                                       10