A new theoretical model of axial crushing of cylindrical tubes with corrugated surfaces has been developed in which the crushing force is analyzed by considering the equilibrium of work done by the crushing force and the energy required to deform the tube. The energy absorbed by the cylindrical tube being crushed is taken to be the sum of the bending energy term and the membrane energy term, which results from compression or extension of a tube wall in the radial direction. The analysis results of the model predict two different modes, termed P- and S-modes, may occur in the collapse of cylindrical tubes with corrugated surfaces. In the P-mode, the compressive force oscillates with folding one after another, whereas in the S-mode the compressive force increases monotonically. Both the mode classification charts and the average crushing force predicted by the developed model are found to be in good agreement with FEM numerical calculation results. In addition, it is found that the increase in the compressive force load for the S-mode is principally due to an increase in the bending energy with deformation.