The numerical study of high-rate plasticity of Cu target with different grain sizes under the action of nanosecond relativistic high-current electron beam has been carried out in the paper. The model of microcrystal material plasticity includes dislocation kinetics and dynamics as well as the stress relief in the grain boundaries of the polycrystal. This model has only two adjustable parameters. The presented results demonstrate a strong dependence of the shock wave attenuation coefficient on the grain size. At the grain size of about 70 nm, the plasticity mechanism of the dislocation glide inside grains changes to plasticity mechanism along grain boundaries. (C) 2011 Elsevier B.V. All rights reserved.