<PAGE>   1

                        STERLING CHEMICALS HOLDINGS, INC.
                                  EXHIBIT 11.1
                         EARNINGS PER SHARE COMPUTATION
                  (Amounts in thousands, except per share data)

<TABLE>
<CAPTION>
                                                                   Three          Three          Nine          Nine
                                                                  Months         Months         Months        Months
                                                                   Ended          Ended          Ended         Ended
                                                                  6/30/98        6/30/97        6/30/98       6/30/97
                                                                ----------     ----------     ----------     ----------
<S>                                                             <C>            <C>            <C>            <C>
     BASIC EARNINGS PER SHARE

Weighted average of common stock outstanding ...............        12,185         11,420         12,007         11,047

Net Loss ...................................................    $  (13,118)    $   (9,377)    $  (39,551)    $  (24,386)
Less: Preferred dividend requirements and accretion ........          (607)          (249)        (1,826)          (411)
Add: ESOP fair market value adjustment (1) .................            --             --            505             --
                                                                ----------     ----------     ----------     ----------

Net loss used in basic loss per share ......................    $  (13,725)    $   (9,626)    $  (40,872)    $  (24,797)
                                                                ==========     ==========     ==========     ==========

     BASIC LOSS PER SHARE ..................................    $    (1.13)    $    (0.84)    $    (3.40)    $    (2.24)
                                                                ==========     ==========     ==========     ==========

     DILUTED EARNINGS PER SHARE

Weighted average of common stock outstanding ...............        12,185         11,420         12,007         11,047

Total weighted average shares outstanding used in
     diluted loss per share computation (2) ................        12,185         11,420         12,007         11,047

Net loss ...................................................    $  (13,118)    $   (9,377)    $  (39,551)    $  (24,386)
Less: Preferred dividend requirements and accretion ........          (607)          (249)        (1,826)          (411)
Add: ESOP fair market value adjustment (1) .................            --             --            505             --
                                                                ----------     ----------     ----------     ----------


Net loss used in diluted earning per share .................    $  (13,725)    $   (9,626)    $  (40,872)    $  (24,797)
                                                                ==========     ==========     ==========     ==========

     DILUTED LOSS PER SHARE (2) ............................    $    (1.13)    $    (0.84)    $    (3.40)    $    (2.24)
                                                                ==========     ==========     ==========     ==========
</TABLE>


 (1) This amount reflects the impact of the changes in the estimated fair
     market value of the Company's Employee Stock Ownership Plan ("ESOP")
     shares that have been released to plan participants.

 (2) Due to losses resulting in anti-dilution, same as amount used in basic
     computation.