The work aims to analyze and obtain the approximate analytical solutions for dropping shock response of nonlinear packaging system. A new nonlinear analytical technique was introduced. Cubic nonlinear and corrugated board hybrid nonlinear dropping shock models were selected as examples and the approximations were obtained by analysis. The original governing equation needed no simplification. The approximation accuracy was increased with the improved approximate orders. The method was still valid to strong nonlinear problems. This research provides a new analysis technique to the dropping shock response of nonlinear packaging system.