A nonlinear wagon–track model on curved track has been developed to characterize rail corrugation formation due to self-excitation of the wheel–rail stick–slip process. In this model, wagon movements were described using up to 78 degrees of freedom (DOFs) to model a three piece freight bogie. Innovatively, the wheelset movements are described using nine DOFs, including torsional and bending modes about the longitudinal and vertical directions. The track modelling is considered as a one-layer structure (two rail beams on discrete spring and damper elements). The wheel sliding after creepage saturation is considered in the wheel–rail interface modelling. Simulation of a case study shows that the frequencies of the wheel stick–slip process are composed of the basic frequency, which might come from the combined effect of sleeper-passing frequency and one third of the combined torsional and bending frequency of the wheelset, and the double and triple basic frequencies, which form the wavelengths of rail corrugation at different situations.