Abstract <p>A normal contact force model is proposed to describe the elastic aftereffect phenomenon of viscoelastic materials under low-speed impact. The model considers the damping effect of the material during the restitution phase and can effectively simulate the contact impact of viscoelastic materials with elastic aftereffect. When deriving the key parameter hysteresis damping coefficient in the normal contact force model, an exact implicit solution for the hysteresis damping coefficient is theoretically obtained based on the precise numerical relationship between relative deformation and relative velocity. The effectiveness of the normal model is verified by the impact test results of the published superball, and is also compared with Wang and Hua model. The results indicate that the normal model is much closer to the experimental results than Wang and Hua model, especially in the restitution phase. Compared with the remaining surface deformation, the restitution coefficient has a more significant effect on the dynamic behavior of the system.</p>