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It is known that more than two thirds of road accidents between moving vehicles are car crashes, where the percentage of human casualties and direct societal losses is comparatively the highest one. Considering the expert-judicial practice the authors view is that the research effort should be put on the development of the mathematical models for an identification of the crash, aiming at the determination of the velocity characteristics of the involved vehicles as well and identification of the places of the passengers in the car before accidents. The study offers mathematical modelling of a car crash caused by a rear impact. It is based on the description of dynamic motion processes of multibody systems, which are configured after car collisions. The mathematical model is constructed for identification of the vehicle kinematic and dynamic characteristics of the running collision different stages.