The Author analyze the transitional mode of movement of a passenger train caused by sudden braking by the driver. To study the possibility of derailment of passenger cars, a simulation model of the movement of a train consisting of a locomotive and twenty passenger cars was developed in the Universal Mechanism software environment, designed to study the dynamics and kinematics of mechanical systems, which include railway rolling stock. The developed model allows taking into account the longitudinal, transverse and vertical vibrations of all cars and locomotive. All bodies in the model are assumed to be absolutely rigid. The assumption of non-deformability of the bodies is based on the fact that the stiffness of the spring suspension and elastic connections is significantly less than the structural rigidity of the bogie frames and the bolster structure, and the frequency of elastic vibrations of these bodies is much higher than the frequency of their vibrations on the spring suspension. Passengers and cargo in a wagon are considered to be non-deformable and integral with the wagon body, similarly in the case of a locomotive body. Between the elements of the system, connections are involved that regulate certain relative movements of these elements.