This paper deals with the optimum structural design of circular cylindrical shells reinforced with identical uniformly spaced T-ring stiffeners, and subjected to external pressure loading. The optimization problems considered are of three types: 1) minimum-weigh t design, 2) design for maximum separation of the lowest two natural frequencies, and 3) design for maximum separation of the lowest two natural frequencies which have primarily axial content. Gross buckling is precluded by specifying a minimum natural frequency, and additional behavioral constraints preclude yielding or buckling of panels, T-ring stiffeners, and web and flange instabilities within each T-ring. The analysis is based on use of an equivalent orthotropic shell model, and optimization is accomplished through use of a sequential unconstrained minimization technique. Examples indicate that moderate increases in weight above optimum (minimum) values can result in more than a doubling of the frequency separations, and that maximum frequency separations are obtained when second and third lowest frequencies approach each other. (A], df