In order to analyse the spacial structures or plane structures subjected to the combined twisting and bending moment, it needs, first of all, to know the callapsing condition of structural sections which leads to the interaction curve between twisting moment and bending moment on the shapes. As examples, three cylindrical sections were prepared for the purpose, that is, elliptical shape, prolate circular shape and patent shape. Experiments were carried out on the three sections above mentioned by applying various twisting moments, while bending moment was kept constant. Upper and lower bound of theoretical solutions were calculated and compared with the experimental results. The following were obtained conclusively. (1) Theoretical curves coincided well with the test results except λ=∞ (λ is the ratio of rate of curvature to rate of twist). (2) It is concluded from the theoretical calculation that collapse load per unit volume is the largest in the case of patent section, and followed by prolate circular shape and elliptical section successively. (3) The difference between upper and lower curve is small if the ratio of thickness to diameter of section is smaller than that of the specimens used. So, it may be said that the use of lower bound theorem is suitable for the design purposes, because of easy calculation and of giving lower or safty values.