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We propose a new approach for railway path diagnostics on the basis of track line stress–strain analysis using the data provided by high-precision accelerometers. This type of sensor provides sufficient accuracy with lower costs, and enables the development of a railway digital twin, according to the concept of the Internet of Things. The installation of sensors on a railway track along its entire length allows real-time monitoring of the states of the technical parameters of the railway track, and using mathematical methods to evaluate its wear on the basis of constantly received data. This paper presents an original 3D model of a railway track line and the results of its analysis using a finite element method. To test the model, we performed an analysis of the normal stresses and deformations in the elements of a railway track by simulating the impact of rolling stock on a section of a railway track with intermediate rail fastenings, ZhBR-65SH. The research results were probated and tested at the testing ground of the Kuibyshev branch of Russian Railways, the Samara track. The proposed approach makes it possible to determine the load of the track, and knowing the movement of the rail, to calculate the structural stress in the elements of the railway track, to constantly monitor the parameters of the slope and rail subsidence.