The paper proposes an analytical method for calculating a long cylindrical shell supported by two identical side elements and loaded with vertical load. The case when the shell is hinged on curvilinear edges is considered, and recommendations for taking into account other boundary conditions are given. No restrictions are imposed on the shape and dimensions of the cross-section of the side element. The proposed algorithm assumes the possibility of implementing two approaches - calculation according to the general semimoment theory and calculation with simplifying hypotheses for flat shells of medium length. In the presented work, the first approach is considered. Mathematically, the problem is reduced to a system of four linear equations. By solving this system, it is possible to determine the forces and displacements due to the action of additional boundary forces, and by adding them with the corresponding components of the momentless stress state, one can obtain the total forces and displacements in the cylindrical shell.