A computationally efficient analysis approach is developed to predict buckling load of geodesically stiffened composite panels under in-plane loads. The analysis procedure accounts for the contribution of the in-plane extensional and out-of-plane bending stiffnesses of the stiffeners through the use of Lagrange multipliers in an energy method solution. The analysis is used to isolate the effect of various stiffener deformation modes on the buckling load and skin deformation patterns of geodesically stiffened panels under various load combinations. The analysis routines are then coupled with the numerical optimizer ADS to create a package for the design of minimum-mass stiffened panels, subject to constraints on buckling of the panel assembly and material strength failure. Material failure in the skin and stiffeners are estimated using a maximum strain criterion. The design variables that can be used for optimization include thickness of the skin laminate, stiffener thickness and height, and positions of straight stiffeners. Applied loads are uniaxial compression, pure shear, and combined compression-shear. / Master of Science