The application of the new numerical approach for elastodynamics problems developed in our previous paper and based on the new solution strategy and the new time-integration methods is considered for 1D and 2D axisymmetric impact problems. It is not easy to solve these problems accurately because the exact solutions of the corresponding semi-discrete elastodynamics problems contain a large number of spurious high-frequency oscillations. We use the 1D impact problem for the calibration of a new analytical expression describing the minimum amount of numerical dissipation necessary for the new time-integration method used for filtering spurious oscillations. Then, we show that the new numerical approach for elastodynamics along with the new expression for numerical dissipation for the first time yield accurate and non-oscillatory solutions of the considered impact problems. The comparison of effectiveness of linear and quadratic elements as well as rectangular and