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This paper presents a model to explain the dynamic mechanism behind the Black Monday  crash on the New York Stock Exchange. A cusp catastrophe model with a slow feedback flow has been developed for the dynamic relationship between prices and dealers in stock exchanges. It makes use of some of the features observed in the crash, and assumes that excess demand by long-run investors is an external driving force, while that of speculators is part of the internal mechanism of the market. A crash occurs only when speculators hold a large proportion of the market, since any slight perturbation of prices by investors, as they respond to changes in macroeconomics variables, will be immediately amplified by speculators. The slow recovery is effected through feedback of prices according to the dealers’ behavior. The paper also suggests intermediary measures to ensure a stable market until the problems of the budget and trade deficits, the major causes of the crash, are resolved.