In this paper, we discuss the dynamics of a rolling wheel with contact rigidity and slip. We propose the approach, using the distance between the center of the wheel and the contact point as an index to the elastic contact for this problem. We discussed about the generation and disappearance condition of slip with dynamic load and initial vertical displacement, using some results for simple cases. It is shown that contact rigidity influences on the time when slip generates or disappears and duration time of slip. It is also clarified that when the friction force reaches the tangent force after slip, slip does not always stop.