A simple, computationally efficient analysis approach is developed to predict the buckling of geodesically stiffened composite panels under in-plane loads. This procedure accounts for the discrete flexural contribution of each stiffener through the use of Lagrange multipliers in an energy method solution. An analysis is also implemented for the buckling of simply supported anisotropic rhombic plates. Examples are presented to verify results of the stability analyses and to demonstrate their convergence behavior. Analysis routines are coupled with a versatile numerical optimizer to create a package for the design of minimum-mass stiffened panels, subject to constraints on buckling of the panel assembly, local buckling of the stiffeners, and material strength failure. The design code is used to conduct a preliminary design study of structurally efficient stiffened aircraft wing rib panels. Design variables include thickness of the skin laminate, stiffener thickness, and stiffener height. Applied loads are uniaxial compression, pure shear, and combined compression-shear. Two different geodesically stiffened wing nib configurations with increasing numbers of stiffeners are considered. Results are presented in the form of structural efficiency curves and are compared with those for minimum-weight longitudinally stiffened panels and unstiffened flat plates. Trends in design parameters, including skin thickness and stiffener height, stiffener thickness, stiffener aspect ratio, stiffener load fraction, and stiffener mass fraction, are also examined for the geodesic panels under compression and shear. The effects of skin laminate geometry and anisotropy on the local buckling behavior of cross-stiffened geodesic panels are examined using the rhombic plate analysis. / Master of Science