The researches of shock-wave processes in the constructional materials are actual, but carrying out of natural experiments is extremely inconvenient and expensive, and sometimes it is even impossible to replicate. Therefore basically all researches of these problems are reduced to various cases of simulation of processes for high-speed loading of materials in the laboratory circumstances. In the paper we consider following directions of mathematical simulation of processes for high-speed loading of materials that were made on department of physical mechanics of St. Petersburg State University: the simulation of shock-loaded media by using of dynamics of dislocations; the simulation of high-speed loading of media with the account of the relaxation phenomena in a near-surface region; the simulation of propagation of the short elastoplastic impulse in medium under the condition of influence of a weak magnetic field; the generation of mathematical models of deformation and destruction of thin metal rings by a magnetic-pulse method; the simulation of crack propagation during the short-term pulse loading.