In terms of dropping shock response of damped hyperbolic tangent nonlinearity packaging system, this paper discusses effective method for analytic solution. Based on the multi-scale method and Lindstedt-Poincare perturbation method (MSLP), the approximate solution of dropping shock of damped hyperbolic tangent nonlinear packaging system is discussed. Through comparison with the R-K solutions, the results show that the error of linear MSLP approximate solution for acceleration and maximum displacement of small damping hyperbolic tangent nonlinearity system (ζ<0.5) dropping shock is less than 5%. and the calculation error decreases rapidly with the decrease of the system damping ratio ζ, without additional correction for the amplitude and frequency. The linear MSLP approximate solution has good calculation precision, especially for small damping hyperbolic tangent nonlinearity system. This research provides a new and effective method reference for the analysis of such problems.