This study discussed the approximate solution for the dropping shock analysis of nonlinear system, the EPE cushion system. A dynamic system model was set up based on the drop impact test of EPE, and the first-order approximate solution was achieved by the variational iteration method, predicting the system parameters such as the period of dropping shock, the maximum displacement and the acceleration. Compared to the actual measurement results, the relative errors of the drop impact time, the displacement and the acceleration peak value were less than 5%. The variational iteration method for analysis of nonlinear drop-impact response system is universal and provides some reference for the analysis of nonlinear packaging system.