An analytical model of the high-velocity interaction of a rigid mesh with a semi-infinite deformable target, which is modeled by a rigid-plastic body, is proposed. We consider the so-called “normal” impact of the mesh on the target: we assume that at the initial moment and subsequent moments of time the mesh is parallel to the target surface, and the mesh velocity vector is perpendicular to the target surface. The model reproduces the most interesting case when the mesh aperture is comparable to or less than the diameter of the wire from which the mesh is woven. The dependence of the mesh penetration depth on the impact velocity and the geometric parameters of the mesh, which are characterized by one dimensionless parameter equal to the ratio of the wire diameter to the mesh period, is studied. Two versions of the model are considered: with and without taking into accounts the fragmentation of the ejected material of the target. The results obtained on the basis of the proposed model are compared with the numerical solutions based on the complete system of equations of the deformable solid mechanics. Numerical simulations were performed using the LS-DYNA package. The example of the penetration of a steel mesh into an aluminum-alloy target with impact velocities of 1-3 km/s is analyzed. It is shown that the model taking into account fragmentation agrees well with the numerical simulations for the mesh parameter interval , which the lower boundary decreases with increasing impact velocity: for km/s, respectively.