Objective To provide a theoretical basis for the design of cushioning packaging, the dynamic characteristics of two-degree-of-freedom tangent system was studied. Methods A two-degree-of-freedom vibration system was proposed to model the shock response of a class of tangent cushioning system. The effect rules of the mass ratio, the frequency ratio, the damping ratio of joint and the cushion on the maximum response displacement of cushion were studied. Results The results showed that the damping ratio of cushion was the key factor in controlling material deformation due to its noticeable influence on the response, and the effects of mass and frequency ratio were very little. Conclusion Deformation of the buffer pad could be controlled through changing the damping of the buffer material to complete the corresponding cushioning packaging design.