The development of a method to effect the automated minimum weight design of ring and stringer stiffened shells is presented. Membrane theory is used for the shell prebuckling analysis. The buckling analysis is based upon an arbitrary shell of revolution computer program. The structural analysis includes both buckling and yielding modes of failure. The synthesis involves the coupling of an exterior penalty function with a method for the unconstrained minimization of a function comprised of a sum of squares. Results of the application of the method to the design of the Viking Aeroshell cone are presented. The least weight Viking Aeroshell appears to be an all magnesium shell with ring stiffeners of hollow circular cross section. Because the method incorporates a general shell of revolution buckling analysis, it can be readily modified and applied to the design of any axisymmetrically loaded uniformly stiffened shell of revolution for which a membrane prebuckling solution exists.