Abstract: A new type of connecting structure—modified shell of constant strength is presented. By using this type of connecting structure, two adjacent cylindrical shells of different diameter can be smoothly connected and the bending stress at the conjunction section can be reduced significantly. Then, based on bending theory of shells of revolution, the stress distribution is analyzed for the combined shell named “cylinder-modified-cylinder”, composed of two cylindrical shells of different diameters connected by a modified shell of constant strength. As for engineering application, the modified equicohesive shell can be used as a connecting structure and some recommendations on the choice of the geometrical parameters are proposed.