Abstract: An efficient and accurate algorithm is desired for calculating load-bearing capacity of special shaped columns. The numerical integration method in common use currently divides sections into two-dimension meshes, which can obtain the load bearing capacity of special shaped columns accurately. However, there exists confliction between calculation speed and accuracy, especially in calculating structures with many members. In this paper, a new numerical integration algorithm is presented. It combines the analytic solution for individual element and the finite element method by implementing particular meshing technique, and shortens iteration process with a new iteration variable presented. Comparative analysis shows the new algorithm achieves higher speed, higher accuracy and wider application.