Honeycomb paperboard is usually adopted as the cushioning material in the transportation process for electronic products with the critical components of simply supported beam. In order to analyze the failure behavior of this sort of fragile part under impact load, the compression mechanical properties of honeycomb paperboard were studied firstly, with the simplified constitutive equation of honeycomb paperboard obtained. Then the relation between the maximum stress and the peak value of rectangular pulse was solved under the excitation of rectangular acceleration pulse, the constraint conditions satisfying cross-sectional area and thickness of honeycomb paperboard were obtained, and the approximate analytical solution of bending stress of simply supported beam was derived. Finally, the reliability of the analytical method was verified by finite element analysis. The results showed that the stress of honeycomb paperboard in yield stage could be expressed as platform stress, and rate dependency was notable for honeycomb paperboard. The rectangular acceleration pulse was used to replace the actual acceleration pulse transmitted by honeycomb paperboard, and had a high accuracy in solving the stress response of the critical components.