It is presented to solve the hunting limit cycles of railway system with multiple degrees of freedom and strongly nonlinear factors by describing function method(DFM). A nonlinear railway vehicle model with several dry friction factors is developed, and the 16 nonlinear transcendental equations of it are deduced using DFM. The modal characteristics of the hunting limit cycle for the vehicle model are obtained by the software programmed to solve complicated equation set. To verify the accuracy of describing function method, the hunting limit cycles of the model are simulated in time domain, and the results from these two methods have good consistence. This shows that the limit cycles of nonlinear rail vehicle systems with strongly nonlinear factors can be solved with high accuracy and efficiency by DFM, which of value in practical engineering application.