© 2016 Elsevier Ltd. The behaviour of the yield strength of metals is considered from viewpoint of dynamics as a function of the limiting stress and the characteristic time of stress relaxation. Experimental curves of the static and dynamic deformation of the coarse-grained copper, microcrystalline and nanocrystalline nickel are analyzed on the basis of the relaxation model of plasticity (the integral criterion) with a constant characteristic relaxation time. The analytical expressions of the relaxation time as a function of variables that characterizes the internal structure of material are obtained from the model of dislocation slip and grain boundary sliding. The strain rate dependences of the yield strength, which are calculated with the help of both the dislocation model and the integral criterion of plasticity, are compared with the experimental data for copper and nickel in a wide range of strain rates (10-3-1011 s-1). It is shown that the proposed analytical expressions give the relaxation time, which