The damage potential and evaluation method of a tangent nonlinear packaging system with critical component was investigated under the action of rectangular acceleration pulse. The dynamical model of the system was developed, and the numerical results of the dynamical equations were got. Based on the results, the damage boundary curve and damage boundary surface of critical component were obtained. And the effect of the frequency ratio, the damping ratio, the pulse peak acceleration in addition to the defined system parameter on the damage boundary of critical component were discussed. It shows that all of their effects are significant. The results lead to some insights into the design of cushioning packaging.