In this paper, the problem of buckling of a thin elastic cylindrical shell supported by the rings of various stiffness is considered. The Rayleigh–Ritz method is used to obtain the problem’s analytical solution for the case of the simply supported 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, have been found. The solution of the problem of minimizing the mass of a structure at a given critical pressure is obtained. Here are considered the rings with zero eccentricity. The approximate analytical solutions are compared with the numerical solutions obtained by the finite element method.