This paper proposes to model cushioning materials by combining hyperbolic tangent function and tangent function together. Based on the proposed model, the kinetics equations for cushion packaging system under excitation of half-sine acceleration pulse shock have been derived, where the rotation due to product’s eccentricity in center of mass has been taken into account. The law for coupling between rotation and translation is discussed. Numerical analysis shows that it may lead to a certain degree’s excessive packaging and thus causes waste if the rotation effect is not considered in design. The proposed model and the established kinetics equations with consideration of coupling between translation and rotation provide much better description regarding the characteristics of practical cushion packaging systems, and thus can be taken as reference in design optimization for packaging structure. The proposed approach can also be directly applied in analyzing the shock responses of packaging systems with multiple degrees of freedom.