The general instability load of a ring-stiffened, circular cylindrical shell under hydrostatic pressure is determined by analyzing an equivalent orthotropic shell. A set of differential equations for the stability of an orthotropic shell is derived and solved for the case of a shell with simple end supports. The solution is presented in terms of parameters of the ring-stiffened, isotropic shell, and a relatively simple expression for the general instability load is obtained. Some numerical examples and graphs of results are presented. In addition, an energy-method solution to the problem is outlined, and the energy and displacement functions that could be used in carrying out a Rayleigh-Ritz approximation are indicated.