The hull girder ultimate strength of a typical bulk carrier is analyzed using a simplified method based on an incremental—iterative approach. First, vertical bending moment is examined by seven different methods. The moment versus curvature curves and the values of the ultimate longitudinal moments at collapse states are determined for both hogging and sagging cases. Second, the ultimate strength under coupled vertical and horizontal bending moment is accounted. An interaction curve is obtained, which corresponds to the results of series of calculation for the ship hull subject to bending conditions with different angles of curvature. It is found that the interaction curve is asymmetrical because the hull cross section is not symmetrical with respect to the horizontal axis and the structural response of the elements under compression is different from that under tension due to nonlinearity caused by buckling. The angles of the resultant bending moment vector and that of the curvature vector are different in investigated cases. The interaction design equations proposed by other researches are also addressed to discuss the results presented by this study.