The aim of this work was to analyze and get the approximate analytical solutions for dropping shock response of tangent nonlinear packaging system and to improve the accuracy of the solutions by correction, in order to satisfy engineering requirements. He′ s parameter-expanding method (PEM) that is applied to solve general nonlinear vibration problems was used. Taking tangent nonlinear packaging system dropping shock model as an example, the algorithm was modified for solving the dropping shock dynamic equations and the first-order approximate solutions were obtained. A novel solution combining PEM with energy method was proposed and the approximation solution was corrected. The results showed that the maximum displacement response, the maximum acceleration response of the system and the period of the response after correction were very similar to those obtained with Runge-Kutta method, with a relative error of <4%. This research provides a new scientific and effective method for the approximate analysis of dropping shock response of nonlinear packaging system.