The analysis of the stability of slopes made of grains submitted to their own weight and to the maximum seismic force of inertia is presented in this paper. The basic hypothesis is that the stresses are transmitted along linear, conjugated and symmetrical chains of contact forces. The obtained stresses fulfill the differential equations of pseudo-static equilibrium and the boundary conditions, and serve to find the potential slip line. Then, the shear stress as well as the shear strength at a constant angle with the major principal stress are calculated. As the soil is in elastic state, the strength parameters must be reduced to be compatible with the failure of the soil. In granular mechanics, the reduction factor leads to different slip lines whether the initial or the reduced shear parameters are used to define the chains of forces. The results are compared with the experimental and numerical slip lines and the factor of safety as well, reported by several authors, finding a good concordance.