This paper is concerned with the elastic buckling of cylindrical shells with internal rigid ring supports. The internal supports impose a zero lateral deflection constraint on the buckling modes at their locations. An automated Rayleigh-Ritz method is presented for solving this buckling problem. The method can handle any combination of end conditions and any number of internal supports. Moreover, it is simple to code and can yield very accurate solutions. New buckling results for cylindrical shells with a single internal ring support, and under lateral pressure and hydrostatic pressure, are given in the form of design charts. These results should be valuable to engineering designers.