Abstract: is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega-shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non-homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non-homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.