The flexible shells of corner-corner type are often utilized as distribution, vapor belts to distribute medium or expansion joints to compensate the difference of displacement between shell side and tube side due to temperature or pressure in heat exchangers. Corner-corner type can be fabricated for large diameter equipment because of better manufacturing process and space saving. However, at present, the design depends on experience and the primary stress of the outer cylinder. The lack of accurate and integral calculation methods have limited its application and even resulted in safety hazard. In this paper, a mechanical model is established for the flexible shell of corner-corner type and analytical solution including the global stresses, local stresses, stress trend curves and axial stiffness is proposed based on the plate and shell theory. The analytical method is verified by finite element analysis. It is demonstrated that the analytical method is accurate and reliable. It is pointed out that the local stresses of each element should not be ignored. Meanwhile, the stresses may transfer to reverse value along the path away from the maximum stress, which would arise the buckling failure.