In the case of automobile collision, the energy absorption is the most important subject. For that reason, the methods to estimate accurately the amount of energy absorbed in the automobile body are indispensable for vehicle safetiness. The side frame construction has an important function for the energy absorption. As the side member has usually thin-walled offset beam, the energy absorption with the side frame is performed by its bending deformations rather than axial compressions. Although many researches have been made recently on the thin-walled beam energy absorption, almost all of them are related to the thin-walled box beam subjected to compression only. This paper analytically refers to the energy absorption of the axial compressions and the bending deformation given at the collision. As the first step, it assumes on the collapse mechanism, that is, the membrance forces of thin-walled box section does not occur. Consequently, this mechanism is an inextensional deformation consisting of polyhedral surfaces. The limit analysis techniques can be applied to the collapse mechanism, and also the deformation energy is calculatable. As the second step, the load-displacement relations are able to obtain from the first step conclusion, that is, the deformation energy is equivalent to a change in potential energy of external load.