Shock-tests of 1565 aluminum alloy under uniaxial strain conditions show that within local regions of target of 100–200 µm a significant increase in mass velocity occurs. Microstructural investigations of specimens revealed a presence of traces of local deformation in the form of narrow shear bands directed perpendicular to the free surface of the target. Simultaneously an ejection of particles from the back side of the target occurs. The discovered phenomenon correlates with the stochastic character of mesostructure behavior at the mesoscopic scale level. Theoretically, the stochasticity of shock-wave propagation in shock deformed solids is taken into account by using the mesoparticle velocity distribution function which is incorporated into the Klein-Gordon equation. The solution to this equation shows that shock-wave amplitude is determined by the relationship between viscosity and velocity variation of mesostructure.