Abstract: In this paper, the problem of buckling of a thin elastic cylindrical shell stiffened by the rings with various stiffness is considered. The Rayleigh–Ritz method is used to obtain the problem’s analytical solution for the case of the clamped edges of the shell. The parameters of the optimal distribution of the structure mass between the shell and the stiffening ribs, which is required to maximize the critical pressure, are found. The rings with zero eccentricity are considered. The obtained analytical solutions are compared with the numerical solution by the finite element method.