Plastic deformation of samples undergoing Taylor anvil-on-rod impact test is simulated utilising finite element method (FEM). Classical (bilinear plasticity using von Mises stress, Johnson-Cook plasticity model) plasticity models and a new plasticity model based on notion of incubation time of plastic flow initiation are employed to model dynamic deformation of tested samples. In order to verify the obtained solutions, the received predictions are compared to available experimental measurements of deformed sample shapes for two different materials (copper, aluminium) and various initial sample velocities. It is shown that bilinear von Mises plasticity model is not able to provide satisfactory coincidence between the shape of the sample boundary received in numerical simulations and in real experimental conditions. At the same time, models accounting for rate dependency of deformation are providing much more accurate results. Substitution of the concept of «dynamic» yielding stress of a material, depending on the rate of deformation by characteristic time of plastic stress relaxation provides a powerful tool for robust prediction of plastic deformation for a wide range of strain rates. The parameter of the characteristic relaxation time has a clear physical interpretation and theoretically can be evaluated from microstructural studies.