The stability studies of slopes by the classical methods based on the concept of safety coefficient present some insufficiencies. They do not allow the calculation of permanent displacements induced by earth quake. To overcome this limitation, finite elements or finite volumes methods have been developed and introduced in several civil engineering calculation software. But, because the implementation of above methods is complicated, they cannot be used as a design tools but rather as a verification tool. In this paper we shows that simplified dynamic methods for the study of slopes stability under dynamic loads have been developed in the literature and their implementation is very easy, and allow the calculation of irreversible permanent displacements induced by an earthquake, which can be used as a design criterion for slopes or embankments stability.