Abstract: To evaluate the ultimate strength capacity of reinforced concrete sections subjected to combined axial force and biaxial bending, the equilibrium equations between the external forces and stress integration over the section shall be satisfied by modifying the depth and the inclination angle of the neutral axis via iteration process. To improve the efficiency and accuracy of stress integration over cross section, a new fast stress integration algorithm is proposed. In consideration of the stress field to be integrated is defined as a step function, according to the strain distribution across the section, firstly the integration area is decomposed into quadrilateral elements, which shall be further refined into several triangular or quadrangular subdomains; then, the stress integration in each quadrilateral element is performed using Gauss quadrature and second-order iso-parametric mapping method. With the proposed method, calculation can be performed without any modification for original meshes in the iteration process. It is suitable for any arbitrary-shaped cross section, including circular sections or multi-cellular hollow sections. The numerical performance of the algorithm has been extensively validated for a wide range of reinforced concrete sections.