In this work, methods of analysis and models of contacting systems dynamics, including heat generation and wear exhibited by such systems, are presented. It should be emphasised that the methods and mathematical models of contacting systems exhibited by rigid/elastic bodies and heat/wear processes have been so far applied separately. Tribological processes occurring on a contact surface were not taken into consideration in the analysis of the dynamic rigid or elastic body models. On the other hand, most of the introduced models of bodies in contact that took tribological effects into consideration did not allow for their inertia analysis. This study contributes to the development of this field, as the models presented here yield prediction of the behaviour of contacting systems taking into account both mentioned aspects simultaneously. When considered from the mathematical point of view, the method of analysis is reduced to the solution of the system of differential equations describing the velocities of contacting bodies and Volterra integral equation modelling contact pressure. The latter equation is obtained with the use of the Laplace integral transform.