In order to research stochastic reliability of elastic Constraint wheel system，considering track random irregularity and their structure random parameters to establish the elastic wheel system with Hamilton function form of the Ito stochastic differential equation. According to the stochastic averaging method expressed the Ito stochastic differential equation as one-dimensional diffusion process, the stochastic global stability conditions had also been obtained by judging the modality of the singular boundary, the condition of the first-passage behavior iscalculated, and the backward Kolmogorov equation for reliability function and probability density function of the first-passage timeis established. On the basis, combined with the initial conditions and boundary conditions, the first-passage issue is derived, and thenumerical simulation is done. The results show that ，When the energy reaches system storage limit, the reliability of the system performance with the passage of time gradually reduced, and the reliability will be destroyed and the occurrence of first-passage failure when the derailment; continue to increase energy for the system, the moment will be derailed derailed in advance, and may also increase. So in the engineering application, we should transverse vibration energy of vehicle monitoring and control, in order to keep their derailment energy or instability energy, and energy dissipation ability of the system is always greater than the increase of energy system, to ensure the safe operation of rail vehicle, especially is especially important for high speed train.