Two-degree-of-freedom mathematical model of packaging system was established and analyzed. A damage evaluation method of a cubic nonlinear packaging system with critical component was put forward. Dynamical equations of the cubic nonlinear packaging system were solved by mathematical analysis. Based on the analysis, the damage boundary curve and damage boundary surface of critical component was obtained. The effect of frequency ratio, damping ratio, and pulse amplitude on the damage boundary of critical component was discussed. The purpose was to provide reference for material selection and structural design of transport package.