The paper presents a plane model of articulated vehicles worked out for the analysis of their dynamics. The dAlambert principle was used for derivation of motion equations for this system. The forces and moments acting on wheels were formulated on the basis of the Dugoff-Uffelmann tyre model. The system consists of any number of vehicles connected by kinematic pair of the 5th class (non friction joint of pivot-bush type) and the fifth wheel (with dry fricton). Since crash calculations usually take into account the impulse of crash force only, and since it is not appropriate for articulated vehicles, a new approach to crash calculation is presented in this paper. The authors propose to calculate the force in crash point both as a function of the relative velocity of vehicles and the stiffness of their bodies. Simulation results of articulated lorry crashes and the attempt to verify the performed simulation are presented in the article.