A new hydrodynamic theory, based on non-equilibrium statistical mechanics is developed to describe the structure formation in dynamically deformed materials. Self-consistent non-local formulation of the boundary-value problem for a high-strain-rate process is reduced to a nonlinear operator set similar to some resonance problems. The branching of solutions to the problem determines both scales and types of the formed internal structure. The theory is applied to the shock wave propagation in solids. The experimentally observable velocity decay proves to be closely connected with such kinetic characteristics as a velocity dispersion and dissipative structure formation. A penetration problem for a long flat rigid plate into a visco-elastic medium is considered accounting for the dynamic structure formation following the high-rate straining in the framework of the non-local self-consistent approach. The approximate solution has shown that the mesoscopic structures formed during the initial stage of penetration can effect on the steady-state stage.