Abstract: The vibration problem generated by urban rail transit has become more and more non-negligible with the rapid development of urbanization. In order to better analyze and solve the effects of vibration, this paper establishes a model of a continuously elastically supported infinitely long rail beam and studies its vibration phenomenon under variable speed moving load. Then, the fourth-order nonlinear differential equation solution problem is transformed into a constant solution problem by Laplace transform combined with Fourier transform, and then the analytical solution of the beam vibration in time and space is obtained by the inverse transformation of Laplace and Fourier. Mathematica and Matlab software are used to calculate the variation law. The results show that the dynamic response of the infinitely long Euler beam is the same at different positions under constant velocity and no damping of the system, and the acceleration of the load movement have an effect on the deflection of the beam.