Purpose. The tasks of modeling the interaction of track and rolling stock are basic ones for most areas of mo-dern scientific research of railway transport. The compilation of the model by the principle of Lagrange d'Alembert has found a very wide application for solving the problems of rolling stock dynamics. Representation of the railway track in the model of crew movement can be implemented in several ways, which, among other things, will differ in detail. The purpose of this work is to create a methodology for representing the railway track in mathematical mo-dels of interaction with rolling stock and obtaining practical results for different characteristics and design of the track and the level of maximum speed. Methodology. The problem consists of determining such characteristics of the path as the reduced mass, the stiffness coefficient, and the dissipation coefficient. As a tool for solving this problem it was used the model of the stress-strain behavior of the railway track based on the joint use of the elastic wave propagation equations to describe the geometry of the outline of the part of the system space that is involved in the interaction at a given time and the equations of dynamic equilibrium of its deformation. This makes it possible to take into account the dynamics of the deflection of the under-rail base, which is especially important for the conditions of passenger traffic, which can be carried out at high speed. Findings. Theoretically justified stiffness and dissipation coefficients of the railway track for calculating the dynamics of rolling stock in modern models based on systems of equations in accordance with the Lagrange d'Alembert principle are obtained. The established va-lues, in contrast to those given in other sources, have a reasonable dependence on the design of the path and the speed of movement. Originality. The approaches of railroad track representation in models of rolling stock described by systems of equations by the Lagrange-d'Alembert principle are expanded. A method for determining the characteristics of the railway track for such models is developed based on the results of variant calculations of the dynamic deflection of the rail from the passage of the wheel. Practical value. The values of the stiffness and dissipation coefficients of the railway track are obtained depending on the design and speed of motion for practical use in appropriate models of interaction between track and rolling stock.