The equations of three-dimensional frictional impact between wheel and rail are formulated, and the instantaneous velocities after collision are deduced according to the rigid-body collision mechanics. The change of tangential relative velocity during collision is discussed. The wheel jumping derailment criterion, which includes the wheel critical lateral impact velocity and the derailment formula related to the maximum wheel lateral force, wheel load and impact duration, is derived according to the kinematics and the law of energy conservation. Parametric analysis shows that: the threshold of derailment can be obviously improved by increasing the flange angle, friction coefficient and effective height of flange; the bigger the flange angle is the smaller the critical friction coefficient will be when stick takes place between wheel and rail; the risk of derailment will be increased because the tangential force of friction which can prevent the wheel from derailment is weakened by the wheel longitudinal relative velocity.