Objective Targeting at single freedom undamped Duffing equation, the He,s frequency-amplitude formulation (HFAF) was used to give approximate solutions for dropping shock response of cubic nonlinear packaging system. Methods Taking the cubic nonlinear packaging system as the study object, He’ s frequency-amplitude formulation (HFAF) was used to analyze the dropping shock response of the system, to obtain the approximate solutions of dropping shock response. In order to improve the accuracy of the solutions, a novel solution combining HFAF with energy method was proposed, the maximal dropping shock response acceleration and displacement of the system were obtained with energy method, and the approximation solution was corrected. Results The results showed that the cceleration-time and the displacement-time curve obtained by this method were very similar to that obtained by Runge-Kutta method, with relative error of < 0.1%. The HFAF method was shown to solve effectively, easily and accurately for the dropping shock problem of nonlinear packaging system with approximations converging rapidly to accurate solutions. Conclusion The results of this research provides a new simple and effective method for the analysis of dropping shock response of nonlinear packaging system.