Some basic mathematical facts pertaining to " Catastrophe Theory" are sketched. The alleged applications to the social sciences are studied. Three representative models, due to E.C. Zeeman, are described in detail, and critically analyzed. The models are found to be vaguely formulated, to be based on false hypotheses, to lead to few nontrivial predictions. Moreover, most of those predictions do not agree with reality. Finally, the only nontrivial mathematical result used in these models - Thom 's theorem - is found (...) to be incorrectly applied. It is concluded that no justification exists for the claim that Catastrophe Theory can be applied to the social sciences. (shrink)