Recently, high strength steel is used increasingly for plates which constitute the frame structures of vehicles. Since these plates become thinner, the buckling on the plates has been recognized as an important issue for automotive industries. For this issue, various methods have been proposed and are currently in practical use. In this paper, regarding bending buckling of box beams which have the rectangular cross-section with four thin plates, we try to derive the buckling stress based on the energy method. The main target of box beams has the aspect ratio of cross-section accompanied with compression buckling in the compressed plate. The bending buckling stress of box beams is derived in two cases of prescribed buckling modes. In first case, it is supposed that the buckling occurs at three sides subjected to compression and bending stresses. In second case, it is supposed that the buckling occurs only at the compression side and forced displacement at two adjacent plates is induced by the compression buckling. And the obtained results of accuracy are compared with the results of buckling eigenvalue analysis using the finite element method (FEM). The results of buckling stress in first case are observed a large difference from FEM results. The reason for this difference is that the buckling deformation assumed for the two surfaces subjected to the bending is much different from FEM results. In second case, the sufficiently practical expression as compared with the FEM results is derived for the buckling stress. So that, the approach shown in this paper is thought to have validity.