The soil reinforcement by geosynthetic is widely used in civil engineering structures: reinforced slopes and walls, embankments on compressible and soft soils, slope on a stable foundation, embankments on cavities and retaining structures, reinforcement in the base layers of railroads and road constructions, bridging over sinkholes or reinforced abutments, piled embankment, reinforced foundation mattresses. The stability of these structures specially depends on the efficiency of the anchors holding the geosynthetic sheets. The anchorages simple run-out and with wrap around are two most commonly used approaches. Designing the required dimensions of the anchorage with wrap around remains problematic. In order to improve the available knowledge of the anchorage systems behaviour, the experimental and numerical studies were performed jointly. This paper focuses on the physical and numerical models of the geosynthetics behaviour in two anchors (simple run-out and with wrap around). Laboratory pull-out tests, performed with two experimental tanks under controlled conditions, consisted in the pull-out of three reinforced non-woven needle-punched geotextiles (uinaxial or biaxial with different stiffness) anchored following various geometries in different kind of soil. In order to confirm and to complete the experimental studies presented in these anchorage systems, a two-dimensional discrete-element model (DEM) was performed. The advantage of the numerical model is its ability to reproduce the behaviour of the geosynthetic and the soil/geosynthetic interaction. The parameters deduced from physical model are used in this numerical study.