Double-twisted hexagonal mesh is used in several fields of civil engineering (gabion structures, retaining nets against rockfalls, etc.). This paper presents an approach based on the discrete element method (DEM) to model this specific mechanical system. Constitutive modeling in finite strains is proposed to take into account the elastoplastic behavior with hardening of the metallic wire mesh. Model parameters are calibrated from a macroscopic point of view by comparing simulations to experimental tensile strength tests performed at the wire-mesh sheet scale. Additional experimental tests, with different mesh sizes and wire diameters, are conducted, yielding valuable data to validate this numerical approach. Lastly, the modeling capabilities are investigated. The simulation of a rockfall-protection structure subjected to an impact loading is presented and the results are discussed from an engineering point of view.