A solution to Gerard's differential equations for plastic buckling of cylindrical shells is found for the case of lobar buckling under hydrostatic pressure. An approximate formula based on this solution is then obtained for buckling in the inelastic region. According to this formula, the buckling pressure is a function of the cylinder geometry and the secant and tangent moduli as determined from a stress-strain intensity diagram for the shell material. Agreement with experiments on ring-stiffened cylinders is found to be within 4 percent.