An interaction of the adhesion forces has nonlinear features which are related to the creep value and strongly depends on the wheel-rail zone condition and track geometry (when driving on a curve section of the track). In many modern mechanical systems torsional structural deformability plays an important role. Often the study of railway vehicle dynamics using the rigid multibody methods without torsionally deformable elements are used This approach does not allow to analyse self-excited vibrations which have an important influence on the wheel-rail longitudinal interaction.