A highly accurate nonlinear analytical algorithm to simulate the behavior of reinforced concrete (RC) columns under monotonic biaxial bending moment and axial loading is proposed. In the proposed algorithm, the nonlinear behavior of confined and unconfined concrete elements as well as steel elements is considered, and the column is discretized into two macro-elements located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections of the column are discretized into a number of rotary oblique fiber elements (ROFEs) and the neutral axis (N.A.) position of each section in each step of loading is searched automatically using a proposed “4-rotations and 2-translations” search model. The ROFEs remain always parallel to the N.A. of the sections and make a uniform stress distribution along each ROFE in each section. Consequently, the variations of stress across each fiber are quite small which increase the accuracy of the calculation, while the number of elements (fibers) is relatively small compared to those of the fixed rectangular finite element (FRFE). This research shows that there is a better agreement between the simulated results using ROFE discretization and experimental results performed in the full-scale RC columns than when the FRFE discretization model is employed. The application of the component effect combination method is also compared with the proposed simultaneous direct method.