Abstract: The issues of studying shock-wave processes in structural materials are relevant; however, it is difficult, expensive, and sometimes even impossible to perform field studies. Therefore, all research on this topic is reduced to various options for modeling the processes rapidly loading materials under laboratory conditions. In the paper, we consider the following areas of the mathematical modeling of high-speed material loading at the Department of Physical Mechanics, St. Petersburg State University: modeling of shock-loaded media using the dynamics of dislocations, modeling the high-speed loading of media with allowance for relaxation phenomena in the near-surface region, modeling the propagation of a short elastoplastic pulse in a medium under the impact of a weak magnetic field, construction of mathematical models of deformation and destruction of thin metal rings by the magnetic-pulse method, and simulation of crack motion under short-term pulse loading.