Railway structures are one of the most important structures in transportation. So the lack of precise study of their dynamic behavior leads to irreparable damages. The significant factors contributing to the accurate analysis of the dynamic behavior of railways are the type of load and foundation used in it. In this study, an Euler-Bernoulli beam subjected to a moving load on a finite depth foundation is presumed. According to the feature of finite beams, just the dynamic equilibrium in the vertical direction is regarded. In this paper, by using equilibrium equations and considering the influence of soil and structure interaction, the physical problem is simulated and by using Fourier transform method the governing differential equations are obtained. Then, the mathematical model based on suggested models is expanded and verified. By assessing the efficiency of the recommended method, the dynamic behavior of the beam is specified and the deflection ratios for various foundations are illustrated. The sensitivity analysis is provided to study the influence of various parameters such as velocity of moving load, elastic foundation depth and damping. Eventually, by considering the sequences of shear waves, critical velocity, which is dependent on the mass ratio, and various kinds of damping, deflection shapes of the beam are attained for the different velocities of the moving load, and the effect of soil depth on the dynamic behavior of the beam is discussed. It is indicated that, foundation inertia leads to a considerable reduction in critical velocity and can also intensify the response of the beam.