The meaning and function of restitution coefficient were introduced， and some kinds of impact process models were analyzed. By deriving the relationship between the restitution coefficient and the model parameters， the energy dissipation was described as restitution coefficient， and the contact deformation was described as contact stiffness for different models. This also demonstrated the difference and connection between the impact process models and the rigid impact model. Through the numerical simulations of an impact system of falling ball， the derived relationship were verified and these models were compared in view of computation precision， efficiency and micro-contact process.