The soil reinforcement by geosynthetic is used in many types of structures: embankments on compressible soil, slope on a stable foundation, embankments on cavities and retaining structures. The stability of these structures specially depends on the efficiency of the anchors holding the geosynthetic sheets. The simple run-out and anchorage with wrap around are most commonly used. In order to improve the available knowledge of the anchorage systems behaviour, experimental and numerical studies were developed jointly. This thesis work concerns in the first part a three-dimensional physical modelling of the behaviour of geosynthetics in two anchors (simple run-out and anchorge with wrap around). The pull-out tests were performed in a test tank under controlled conditions in the laboratory. In the second part, the parameters of the interaction soil/geosynthetic found from the experimental study were used into the numerical code “FLAC2D” (continuous) for a better understanding of the behaviour of geosynthetics in anchorage. The influence of several parameters on the behaviour of geosynthetic was treated in this numerical study. In parallel with this model, another numerical modelling (discontinuous) by the discrete element method (PFC2D) was carried out. The results of these models are closely to experimental results which confirm the analysis about the anchoring mechanisms.