<PAGE>   1

                                                                    EXHIBIT 11.1

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


<TABLE>
<CAPTION>
                                                          THREE MONTHS ENDED JUNE 30,         NINE MONTHS ENDED JUNE 30,
                                                        ------------------------------      ------------------------------
                                                            1999              1998              1999              1998
                                                        ------------      ------------      ------------      ------------
<S>                                                     <C>               <C>               <C>               <C>
     BASIC EARNINGS PER SHARE

Weighted average of common stock outstanding                  12,516            12,185            12,469            12,007

Net Loss                                                $    (16,415)     $    (13,118)     $    (54,335)     $    (39,551)
Less: Preferred dividend requirements and accretion             (672)             (607)           (1,975)           (1,826)
Plus: Depreciation of value of Released Shares                  --                --               1,048               505
                                                        ------------      ------------      ------------      ------------

Net loss used in basic loss per share                   $    (17,087)     $    (13,725)     $    (55,262)     $    (40,872)
                                                        ============      ============      ============      ============

     BASIC LOSS PER SHARE                               $      (1.37)     $      (1.13)     $      (4.43)     $      (3.40)
                                                        ============      ============      ============      ============

     DILUTED EARNINGS PER SHARE

Weighted average of common stock outstanding                  12,516            12,185            12,469            12,007

Total weighted average shares outstanding used in
     diluted loss per share computation (1)                   12,516            12,185            12,469            12,007

Net loss                                                $    (16,415)     $    (13,118)     $    (54,335)     $    (39,551)
Less: Preferred dividend requirements and accretion             (672)             (607)           (1,975)           (1,826)
Plus: Depreciation of value of Released Shares                  --                --               1,048               505
                                                        ------------      ------------      ------------      ------------

Net loss used in diluted earning per share              $    (17,087)     $    (13,725)     $    (55,262)     $    (40,872)
                                                        ============      ============      ============      ============

         DILUTED LOSS PER SHARE (1)                     $      (1.37)     $      (1.13)     $      (4.43)     $      (3.40)
                                                        ============      ============      ============      ============
</TABLE>

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