PANDA2 finds minimum weight designs of laminated composite flat or curved cylindrical panels or cylindrical shells with stiffeners in one or two orthogonal directions. The panels or shells can be loaded by as many as five combinations of in-plane loads and normal pressure. The axial load can vary across the panel. Constraints on the design include crippling, local and general buckling, maximum tensile or compressive stress along the fibers and normal to the fibers in each lamina, and maximum in-plane shear stress in each lamina. Local and general buckling loads are calculated with the use of either closed-form expressions or discretized models of panel cross sections. An analysis branch exists in which local post buckling of the panel skin is accounted for. In this branch a constraint condition that prevents stiffener popoff is introduced into the optimization calculations. Much of this paper represents a tutorial run through the PANDA2 processors for a hat-stiffened panel under combined axial compression, in-plane shear and normal pressure. Examples follow in which results from PANDA2 are compared with those in the literature and those obtained with the STAGS and EAL computer programs. Results of an extensive study are given for an optimized, blade-stiffened panel design so that it buckles locally at about 10% of the design load. The axially stiffened panel is subjected to pure axial compression, pure normal pressure, combined axial compression and normal pressure, and combined axial compression and residual stresses and deformations that arise from a simulated curing process. An example is provided of a design process applied to a ring and stringer stiffened cylindrical shell similar in geometry and loading to the 2/3 interstage of the ARIANE 4 booster.