Results of experimental research on shock loading of solid materials demonstrate that the revealed dependences of waveforms and threshold of the structure instability on strain-rate, target thickness and state of the material structure cannot be described in the framework of the conventional continuum mechanics. New concept of shock-wave processes in condensed matter is proposed on base of nonlocal theory of nonequilibrium transport which allowed a transition from the elastic medium reaction to the hydrodynamic one depending on the rate and duration of the loading. A new mathematical model of elastic-plastic wave is constructed to describe the elastic precursor relaxation and the plastic front formation taking into account the changing оf material properties during the wave propagation. Analysis of experimental waveforms shows that for the shock-induced processes it is incorrect a priori to divide the components of stress and strain into elastic and plastic parts. The model allowed accounting for the inertial medium properties under short-duration loading and selforganization of new internal structures.