The analysis of plastic deformation of metals and polymethylmethacrylate under dynamic loading is carried out using a relaxation model of plastic deformation. The invariance of the parameters of the relaxation model of plasticity to the strain history allows us to obtain any set of deformation curves from a united viewpoint, both monotonic, with varying yield strength, and non-monotonic, with emerging and varying yield drop, as it is observed in experiments. The increase of the yield strength of high-strength 2.3Ni-1.3Cr steel together with the hardening effect both under high-rate and slow deformation is also modeled on the basis of the relaxation model. Using DP600 steel and nanocrystalline nickel as an example it is shown that the relaxation model of plasticity allows one to predict a smooth transition to the plastic deformation stage at slow quasi-static effects of ~ 10–3 s – 1, and also the appearance of a yield drop effect at strain rates of 500–6000 s –1. It is also shown that the developed approach allows one to simulate similar effects under high-rate deformation of polymethylmethacrylate. Thus, it was demonstrated using specific materials as an example that it is possible to effectively predict the deformation dependencies of the materials studied in a wide range of strain rates of 10-4-104 s-1 based on the parameters of the relaxation model of irreversible deformations.