Anchored wire meshes are commonly adopted to stabilize potentially unstable soil slopes. This reinforcement technique, employed either as an active or a passive anchoring system, is commonly designed according to ultimate limit state approaches. In this paper, an interaction model, useful for the design of anchored wire meshes, is proposed. The model is based on the results of a series of 3D large displacement finite element numerical analyses, in which the wire mesh mechanical behaviour is modelled as either an elastic or an elastic–plastic membrane. The model is inspired to standard load–displacement curves for shallow foundations, and the wire mesh presence is taken into account by suitably modifying the bearing capacity formula. The proposed model predictions are compared with experimental punching test results. The use of the model, only requiring the definition of geometry and soil–wire mesh mechanical properties, allows the pre-design of the reinforcement system without performing ad hoc finite element numerical analyses.