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The paper corrugation tube is an attractive and innovative mode of cushioning protection and energy absorption for the general protection and packaging technology of military and civil products. The aims of this paper focus on the dynamic compression characteristics of four kinds of regular polygonal paper corrugation tubes under the conditions of axial drop impacts, and the influence rules of structural parameters and load parameters on the dynamic cushioning energy absorption. The results show that, the tube direction has a crucial effect on the deformation mode of the paper corrugation tubes, the deformation of X-direction paper corrugation tubes has a stable accordion mode, but that of Y-direction paper corrugation tubes is a mixture of steady progressive buckling and other non-ideal modes. The X-direction paper corrugation tubes have lower peak stress, stable and controllable deformation mode with multiple folds, and higher total energy absorption, unit area energy absorption, specific energy absorption and stroke efficiency than the Y-direction paper corrugation tubes. Moreover, the change of cross-section shape of X-direction paper corrugation tubes has no obvious influence on the total energy absorption, while the total energy absorption of Y-direction paper corrugation tube obviously rises with the increase of the number of cross-section edges of the tubes, but the unit area energy absorption, specific energy absorption and stroke efficiency decrease with the increase of the number of cross-section edges of the tubes. Moreover, the increase of the number of cross-section edges of the tubes made the total energy absorption of Y-direction tubes rise, while the total energy absorption of X-direction tubes has no obvious change. But the unit area energy absorption, specific energy absorption and stroke efficiency decrease with the increase of the number of cross-section edges of the tubes. Furthermore, the tube length, impact block mass and impact energy have also important influence on the cushioning energy absorption of the paper corrugation tubes under axial drop impact.