The work aims to propose an approximate analytical solution for the drop shock system by using the NHB method with the tangent packaging system with linear damping as the research object. Firstly, the drop impact dynamics equation of the system was established. Secondly, the dimensionless parameters-displacement and time-were introduced. Afterwards, the approximate analytical solution of the system response was obtained by using the NHB method after linearization. Thirdly, the expressions of the maximum displacement, peak acceleration and duration were further obtained. Finally, the calculation accuracy of the proposed algorithm was confirmed by case study.The comparison between the proposed NHB method and the R-K method showed that the average value of relative errors of displacement and acceleration obtained by the proposed method was controlled within 6%. The damping coefficient significantly affected the response of the system. Following the increase of the damping coefficient, the peak displacement decreased. Meanwhile, the peak time and oscillation frequency of the system decreased to some extent. The NHB method is suitable for solving the drop shock response of tangent packaging system with linear damping.