Abstract: In this paper, the stability analysis of the slope has been studied by the explicit Lagrangian difference method for the continuum body using shear strength discount. In some case study, it is shown that the horizontal displacement of the slope top will be increasing rapidly when the reduction factor reaches a certain value.According to this phenomenon, a criterion has been proposed, which is used to distinguish the collapse of slope .If this criterion, which is the ratio of the horizontal displacement increment of the slope top and the increment of reduction factor, is larger than some suggested value sc then the slope is in failure state.Therefore the non-convergence or other indistinctness will not be used as criterion to identify slope failure state when slope stability analysis is done using the shear strength discount method.This criterion has the clear physical meaning and is objective and explicit, and easily to be implemented in analysis. Compared with the limit equilibrium methods, such as Swedish slip-circle method, simplified Bishop method and Spencer method, it is shown that the sliding surface of this method is coincident with those of other method basically. It is explained that the method and the criterion of the "failure" state proposed in this paper is appropriate.The influence of dilative angle on stability factor is also discussed, and the conclusion has been got that the stability factor of the slope would be overestimated if the associate plastic flow rule is adopted.