Ring-stiffened cylindrical shells are used in offshore and submergible structures which are exposed to the external pressure. There are two cases where the ring stiffener is attached inside or outside to the cylindrical shell. At the stage of initial design, several formulas have been used to estimate the shell buckling strength and the overall buckling strength of ring-stiffened cylindrical shells. However, as for the overall buckling strength, these formulas give smaller buckling strength of the inside ring-stiffened cylindrical shell and larger buckling strength of the outside ring-stiffened cylindrical shell than the calculation result obtained by FE analysis. In this paper, a new formula for estimating the elastic overall buckling strength of ring-stiffened cylindrical shells is derived and proposed based on the equilibrium of the circumferential force and the moment considering the change of the circumferential bending rigidity due to the effect of the curved member as well as the shearing deformation. Moreover, the accuracy of the proposed formula is verified by comparing with the calculation results by FE analysis.