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The article considers the dynamic processes of the oscillatory system «wagon - way», its mathematical model is formed and its features are established. The analysis of existing approaches to the consideration of the influence of dissipative forces on the stability of rolling stock is carried out, their shortcomings are revealed. When composing dynamic process equations, it is important to proceed from their exact expressions when considering kinetic and potential energy, i.e. to take into account the relationship between generalized coordinates, which will allow us to consider in detail the process of rolling stock oscillations. The zone of autoparametric resonance is found. It is established that dry friction forces do not interfere with parametric resonance. Dynamic equations are compiled taking into account the scattering forces arising in the contact points of the structural elements of the car. The influence of dry friction forces on the critical coefficient of parametric excitation is determined. The areas of dynamic instability of a car when moving along a railway track with different characteristics are determined. The features of the behavior of the system under the influence of dry friction forces are revealed. It is established that dry friction forces do not reduce the amplitude of bouncing and can lead to an increase in lateral pitching vibrations due to energy pumping.