Geosynthetics are used as reinforcing elements in a wide variety of structures: reinforced slopes and walls; embankments on soft soils; piled embankment; reinforcement in the base layers of railroad and road constructions; reinforced foundation mattresses; bridging of sinkholes or reinforced abutments. In some cases, these reinforced structures require anchorage areas. Designing the required dimensions of this anchorage remains problematic. This paper focuses on the simple run-out and wrap around anchorages. Laboratory tests, performed with these two anchorage benches, consisted of the pull-out of three geotextiles (uniaxial or biaxial with different stiffness) anchored following various geometries in different kinds of soil. In order to confirm and to complete the experimental studies presented in these anchorage systems, a specific two-dimensional discrete-element model has been used. The soil was described by discrete elements and the geosynthetic behaviour was taken into account by the use of thin finite elements. The interface behaviour between the soil particles and the geosynthetic elements was considered at each contact point by using a Coulomb contact law. The numerical model reproduced the experimental campaign and the anchorage mechanisms reasonably. The load transfer between the geosynthetic and soil was visualised by the force and displacements distribution along the geosynthetic sheet. The numerical procedure could also be used to define the conditions of stability for reinforced slopes or walls.