Numerical method, in particular the finite element method, is a powerful tool to analyze the dynamic response of the vehicle-track coupling system, and the key to solve the complicated dynamic interactions between the vehicle and the track is to construct a reasonable model for the track structure and the vehicle. As the basis for establishing the dynamic analysis model of various vehicle-track coupling systems, the fundamental concepts of the dynamic finite element method (FEM) and the numerical algorithm for 2D beam elements are introduced. A computationally efficient and easily programmable generalized beam element model for the track structure is presented. Beginning with a simple single-wheel vehicle model incorporating a primary suspension system, the analysis progressively describes half-vehicle and full-vehicle models equipped with both primary and secondary suspension systems. The corresponding dynamics equations for each vehicle model are derived.