Within the framework of the exact formulation of the problems of continuum mechanics, problems of dynamic impact on man are considered. Particular attention is paid to the impact on the «head-helmet» system. The dynamics of the zones of destruction of the protective structure at various impact rates is shown, the values of the most important dynamic and kinematic characteristics at various characteristic points of the «head-helmet» system are obtained. Developed for solving dynamic problems, application software allows you to study the behavior of various protective composite barriers for various impact impacts and to have information about the values of any kinematic and dynamic quantities at any points of the system at any one time. The proposed approach and applied software allow to consider and carry out a full analysis of dynamic effects on structures whose materials have various complicated properties: softening, variable elastic properties, irreversible volume deformations, cross effects of the first two invariants of stress and strain tensors, in particular dilatancy and Etc. [1-5]. All this makes it possible to predict the processes of deformation and destruction for a wide class of dynamic problems; while the cost of expensive experimental research is significantly reduced. In the present paper, the analysis is carried out in the framework of an axisymmetric formulation. To describe irreversible deformation, the generalized model of Mises plasticity is applied, and the plasticity limit can both grow and decrease to certain limiting values characterizing the destruction. Defining relations for irreversible deformations are formulated in the space of deformations and give the opportunity to describe both hardening and softening. A complete system of differential equations describing the dynamic processes in the studied bodies is given. On the basis of the finite element method, an effective numerical scheme for calculating the tasks is proposed and implemented. The results of calculations for two characteristic velocities of impact loading are presented: 60 km/h and 200 km/h. It is shown that at 60 km/h irreversible deformations occur only in the helmet, and at 200 km/h the helmet, cranium and skull base are destroyed.