In the paper the particular problems of modelling and simulation of dynamic unilateral contact of compact hard bodies are considered. Special attention is given to the rolling contact of bodies with irregular rolling surfaces. Due to inertia of the bodies and large but finite contact stiffness, contact vibrations arise and transient contact discontiuities may occur. In the developed algorithms, Hertzian model of contact is used within the elastic range. Two different quasi- static models of contact are used whenever during simulation the dynamic contact force exceeds its limiting value for the first plastic flow. The modelling problems considered herein are plastic deformations resulting form free excessive vertical oscillations are proposed as one of the possible causes of rail and wheel corrugations.