The model of propagation of the steady elasto-plastic wave based on the dynamics of dislocations was supplemented with the relaxation term to conduct investigations. The shockwave experiments, the analytical investigations, and the simulation of dynamic processes by the methods of molecular dynamics revealed an important feature of the dynamic heterogenization of solids. The shock front in the structural-nonuniform medium represented the superposition of two modes of motion and the average motion of the flat front and the quickly fluctuating motion of individual portions with respect to the average motion of the front. The experiments on the shock loading of heterogeneous media revealed the presence of a correlation between the mass-velocity variation and the macroscopic deformation rate.