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The simple relations to assess residual hull girder strength are obtained, which may be used as handy and reliable tools to help make timely decisions in the event of an emergency. Kalman et al(2002) investigated the effect of different damage modes of a hull section on the residual longitudinal strength of an impaired ship based on elastic theory, fully plastic resistance moment theory and ultimate bending moment approach, respectively. The practical application of the computational link between the residual strength contours and ship’s survival is further clarified in given example. Finally, it is suggested that the use of constant, residual strength contours of a damaged hull girder section to enhance assessment of a ship’s survival ability when exposed to longitudinal vertical bending after an accident. Santos et al(2002) presented a probabilistic methodology for assessing the survivability of damaged passenger Ro-Ro ships through the identification of critical damage scenarios. The Static Equivalent Method was used to calculate the critical sea state the ship can survive in a given damage scenario and Monte-Carlo simulation is used to take into account the uncertainties in the ship’s loading condition at the time of the accident: intact draught, vertical and longitudinal position of the center of gravity and permeability of the Ro-Ro decks. From above review on the residual strength of the damaged ship, the research on this field mainly focuses on the following two aspects: 1. Estimating the influence of damaged ship members (such as damaged panels and damaged stiffeners) on the hull girder ultimate strength. 2. Based on the empirical and semi-analytical methods, assessing the residual longitudinal strength of ship after collision and grounding in order to providing handy tools to help make timely decisions in the event of an emergency at cost of accuracy. The objective of this paper is to establish a procedure to evaluate the residual ultimate hull girder strength of damaged ship causing by collision or grounding with considering the asymmetry of cross section and the instantaneous shift of neutral axis due to the local structure damage. Method and the interaction between the vertical and horizontal bending moment In this research, a simplified progressive collapse analysis based on the Smith method (Smith, 1977; Dow & smith et al., 1981) is performed. The stress-strain relationship of element in the simplified method is determined on the basis of a rational theoretical background. The vertical bending moment is indeed the most important load effect when considering the hull girder collapse. However, in many types of ships, the combined effect of the vertical and the horizontal bending moments is important especially after the ship is damaged. As in the case of biaxial compressive strength of the plates (Guedes Soares, C. & Gordo, J. M. 1996), the nature of the interaction problem requires the solution of two issues. One is the collapse load in each inpidual mode, which will be used as normalizing factor in the interaction formula. The second problem is the interaction formula itself in order to adequately describe the combined effect of vertical and horizontal collapse moments. The problem of the interaction relation for collapse of hull sections under combined loading was addressed in a preliminary study by Gordo Soares and Guedes (1995) who analyzed the case of four single skin tankers. Mansour et al (1995) also studied the problem although using a different method to predict the collapse load and a different interaction formula. Laterly, Gordo and Guede Soares (1997) extended their early work by considering five additional tankers with different configuration with double hull and with double bottom. Furthermore, in order to cover the range of representative hull types, six container ships, are also including in the calculation.