A method for the computation of the Interaction Surface of reinforced concrete sections subjected to axial load and biaxial bending is developed. The method is exact and it is based on the transformation of the double equilibrium integrals into line-integrals along the compressive perimeter of the concrete section using Green's Theorem. For up to third degree polynomial stress-strain relations for concrete. Gauss integration with only three sample integration points yields exact results. This is the reason why the method is computationally efficient. Note that the concrete stress strain relations recommended by the American Concrete Institute and by the Eurocode 2 of the European Union, both fall within the above limitation. The method is demonstrated by a numerical example.