Two-degree-of-freedom nonlinear packaging system model was established. The shock dynamic equations were obtained and their numerical solutions were solved. The shock response characteristics of hyperbolic tangent packaging system with critical component were investigated. The rectangular acceleration pulse was chosen in the experiment due to its highest severity among all kinds of pulse. The influences of frequency ratio, amplitude of pulse excitation, damp, and system parameters on shock response of critical components were studied. The results showed that frequency ratio, amplitude of pulse excitation, damp, and system parameters all have significant influence on the peak value of shock response of critical components. The purpose was to provide reference on cushion packaging design.