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This paper presents a new computer method for the rapid design and ultimate strength capacity evaluation of composite steel-concrete cross-sections with arbitrary shape. The proposed approach has been found to be very stable for all cases examined herein even when the section is close to the state of pure compression or tension, and it is not sensitive to the initial or starting values, to how the origin of the reference loading axes is chosen and to the strain softening exhibited by concrete in compression. A computer program was developed, aimed at obtaining the ultimate strength and reinforcement required by composite cross-sections subjected to combined biaxial bending and axial load. In order to illustrate the accuracy and efficiency of the proposed method, this program was used to study several representative examples, which have been studied previously by other researchers. The examples run and the comparisons made prove the effectiveness and time saving of the proposed method of analysis