Some characteristics of crowd jam like the phenomena of discontinuous jumping in reality are hard to be explained by the equations governing pedestrians. The catastrophe theory can explain these characteristics. A cusp-catastrophe model is developed to analyze the mechanics of crowd jam by drawing graphs for a cusp-catastrophe model of crowd, the bifurcation set and the projection of catastrophe model. Meanwhile, the critical density and the critical velocity are derived. It is concluded that the cusp model is a more efficient predictor than the linear model or the equations governing pedestrians and is reasonably realistic for dense crowd flow scenarios.