In the present study, the effect of the radius of railway curved tracks on the slip of a wheel on a rail is studied. A 3D finite-element model of a wheelset-track system is established when the creep force between the wheel and rail is saturated. The occurrence propensity of the self-excited vibration of the wheelset-track system is predicted. It is concluded that the radius of curved tracks has a strong effect on the slip of wheels on rails. In the tightly curved tracks, the slip of the wheel of the leading wheelset on the rail always occurs. The wheelset-track system has a strong occurrence propensity for unstable vibrations on the tightly curved tracks. The accuracy of the rail corrugation prediction based on the unstable vibrations of wheelset-track systems is determined to be 85–90% or higher.