An approach to the ultimate strength calculation and the dimensioning of arbitrarily shaped reinforced concrete sections, subject to combined biaxial bending and axial compression, is presented. The analysis is performed in accordance with the American Concrete Institute (ACI) code. A computer program is presented for rapid design of arbitrarily shaped reinforced concrete members under biaxial bending and axial load. In the proposed method the equilibrium equations are expressed in terms of the three unknowns, e.g. location of neutral axis and amount of total reinforcement area within the cross-section, which lead to three simultaneous nonlinear algebraic equations which are solved by a procedure based on the Newton-Raphson method. One design problem, available in the literature, is solved by this program to provide possible design procedures. A listing of the computer program is given in the Appendix.