A mathematical model to describe the stress-strain state of structures made of orthotropic materials. On its basis, numerically simulated dynamic loading of structures, along the trajectories of small curvature (classification A.A.Ilyushina theory of elastoplastic processes). Plastic deformation of the material described in terms of the flow theory. This model describes the deformation of elastoplastic orthotropic materials with the destruction of the residual deformation of not more than 6%. Such materials include concretes, carbon steels in particular low temperature range of gray cast irons as well as many alloys. The results of numerical modeling of the load obstacles transtropic D16T alloy steel drummer in the range of impact loading rates (400-1200) m / s.