An analysis of rib-stiffened columns is made in the present study, employing the energy method with three sinusoidal terms in the assumed deflection function. A total of 325 design curves are determined and plotted showing the critical load for different lengths, widths and thickness of the stiffening ribs. The curves show an increasing trend in buckling load-carrying capacity up to 250 percent. Minimizing the material volume of the compound columns, the optimal portions of the design curves are determined. Using "NETS", a neural network has been designed which consists of two hidden layers with 15 nodes in each layer. 640 optimum input-output pairs have been selected and used to train the network. The network was successfully trained with a maximum error of 0.0075 and RMS error of 0.0014. The response of the network to new data entries (numerical values not used in the training process) of the variable parameters is examined and compared to those recorded in the design curves . Maximum error for new data entries is less than 4 %.