This paper is concerned with the ultimate strength and reliability analysis of ship's hull girders, which are composed of the spatial membrane elements and subjected to combined static loads and extreme wave loads. The linearized failure condition of an element is first introduced, which takes account of the yielding and buckling collapse under the plane stress condition. The failure criterion facilitates the generation of safety margins and the calculation of failure probabilities. Structural failure is defined as the generation of large deformation due to collapse. The socalled branch-and-bound method is applied to select the probabilistically dominant failure modes, which saves the computational efforts to perform a reliability analysis on large-scale structures. Finally, the proposed methods are applied to spatial plate structures idealized for modelling main hull girders of an oil tanker and a bulk carrier under two loading conditions. Through numerical examples, the properties of proposed methods are investigated.