Based on the Drucker-Prager yield criterion which matches with the Mohr-Coulomb yield criterion under the plane strain condition, this paper sets up a cusp catastrophe model of maximum horizontal and vertical displacements to strength reduction factor by using the cusp catastrophe theory. And the catastrophe criterion of slope failure is quantified to the control variable (u) and discriminant (△) which are evaluated by comparing with zero. Taking the above study as the foundation, the cusp catastrophe model is applied to solve one of the standard test ACADS examples. On the two criterions for slope failure of horizontal and vertical displacements catastrophe model, the safety factor of the slope is 0.988 which is consistent with those by ACAS. It shows that the cusp catastrophe model in slope failure analysis is feasible and practical.