The mass transfer of interstitial impurities in a crystalline lattice under the influence of the fast-moving deformation disturbance of the type of a shock wave is considered. The velocity of the movement of the disturbance is supposed to be compared with the characteristic velocity of the relaxation of the diffusion flux to its local equilibrium value determined by the Fick's law. The similar situation occurs in a number of experiments on the exposure of a solid to dynamical external loads giving rise to such fast hydrodynamical processes in a sample that the local equilibrium assumption, normally assumed for the macroscopic description of transport processes, is no longer valid. Considering the diffusion flux among the set of independent variables we have derived a set of coupled hydrodynamic equations describing nonequilibrium behavior of a solid in the absence of local equilibrium in the system. Within the scope-of the proposed model it has been shown that in comparison with the local equilibrium system an enhanced mass transfer occurs under local nonequilibrium conditions. (C) 2003 Elsevier Science Ltd. All rights reserved.