For the investigation of rail corrugation formation due to the wheel stick-slip process on curved tracks, a nonlinear wagon–track model is presented in this paper. In this model, the wagon movements were described using up to 78 degrees of freedom (Dofs). The two wheels in a wheelset are coupled through the stiffness coefficients corresponding to the natural torsional and bending modes of wheelset. The track is considered as a discretely supported distributed-parameter track modelling with one layer. In the wheel–rail interface, before the creep saturation point µsNc (μs, static wheel–rail friction coefficient; μc, normal force), the creep forces and moments are calculated using Kalker’s linear creep theory. After that point, the wheel slides on the rail and the friction force will be μkNc (µk—kinetic friction coefficient). The simulations show that the frequency of wheel stick-slip process is composed of a basic frequency, which matches the sleeper-passing frequency and the combined torsional and bending frequency of the wheelset, forming the wavelength of rail corrugation at different situations. Generally, the wheel stickslip process on the high rail oscillates at the basic frequency whilst the dominant frequency on the low rail is double the basic frequency. The effects of the curved track parameters, the wheel–rail friction characteristics and the wheel–rail profiles on the wheel stick-slip process were investigated.