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A polynomial model was suggested for precompressed honeycomb paperboard packaging system, and then both of the inner-resonance conditions for packaged product and the critical component were obtained applying the variational approach. Finally, the effect of fatigue damage on the inner resonance conditions was discussed. The results show that both the packaged product and critical component can be damaged by inner-resonance when some conditions required were met, and the fatigue of honeycomb paperboard will obviously affect the inner-resonance conditions.