Geosynthetic systems constitute a preferential slip line when they are laid down on the slopes of civil engineering structures. To improve the design of GLS on slopes under low normal stresses, a numerical model based on the finite element method (FEM) is proposed in this paper. This 2-D model makes it possible to take into account the compatibility of the strains and displacements of the various components in the GLS and the effect of flow parallel with the slope in the cover soil. Two full-scale instrumented experiments are simulated to validate the model presented.