Structural pounding under earthquakes has been recently extensively investigated by using different models of impact force. In this paper, reexamination into the Hertz contact model with nonlinear damping is made. Based upon this reexamination, the formula used to determine the damping constant in terms of the spring stiffness, the coefficient of restitution and relative approaching velocity of two colliding bodies is found to be wrong. In order to correct this error, a more accurate approximating formula for the damping constant is theoretically derived. The correctness of the derived analytical formula has been confirmed through numerical simulations.