The accurate numerical solution of contact-impact problems using finite element method is challenging in multiple aspects. The main difficulty is the effective attenuation of spurious oscillations emerging due to the spatial discretization. As these oscillations deteriorate the accuracy, the elimination of spurious components in the numerical results has a great importance. To achieve it, a damping effect must be contained in the applied numerical scheme. Based on the conducted research in this field, the concrete shape of the damping character plays a crucial role in reducing oscillations with the best possible efficacy. The proposed method operates with viscous damping formulated as Caughey damping. Considering concrete industrial problems, represented as a two-dimensional FEM model, the proposed scheme proved to be effective and more accurate compared to several widely applied numerical methods. Due to the simple formulation combined with good oscillations reduction, the newly developed method has a great potential in practical engineering applications.