Styryl sulfone compounds of the invention selectively inhibit proliferation of tumor cells, and induce apoptosis of tumor cells, while sparing normal cells. The compounds, which are useful in the treatment of cancer and other proliferative disorders, have (a) the formula II: ##STR1## wherein n is zero or one; R.sub.1 is selected from the group consisting of hydrogen, chlorine, fluorine and bromine; R.sub.2 is selected from the group consisting of hydrogen, chlorine, fluorine, bromine, methyl and methoxy; and R.sub.3 is selected from the group consisting of hydrogen, chlorine and fluorine; provided, R.sub.2 may not be methyl or methoxy when R.sub.1 and R.sub.3 are both hydrogen and n is zero or one; and R.sub.1, R.sub.2 and R.sub.3 may not all be hydrogen when n is one; (b) the formula III: ##STR2## wherein R.sub.1 is selected from the group consisting of hydrogen, chlorine, fluorine and bromine; or (c) or the formula IV: ##STR3## wherein R.sub.1 is selected from the group consisting of fluorine and bromine, and R.sub.2 is selected from the group consisting of 2-chlorophenyl, 4-chlorophenyl, 4-fluorophenyl and 2-nitrophenyl.