This paper is concerned with reliability assessment of ship structures which are modeled as relatively rigid frame and subjected to quasi-static extreme loads. At first, a linearized plasticity condition of the section is introduced which takes into account of combined effects of bending moment, shearing force and axial force on the yielding. The failure criterion greatly facilitates generation of the safety margins and calculation of the failure probabilities. Structural failure is defined as large reduction of total structure stiffness. Second, the socalled branch-and-bound method is used to select the probabilistically dominant failure modes, which saves the computational efforts performing the reliability analysis of large-scale structures. The failure probabilities of the selected modes are evaluated. Third, the proposed methods are applied to a plane frame structure idealized for a transverse ring of a tanker. Through the numerical example, the following results are obtained. (1) The linearized plasticity condition is effectively applied to consider the effect of shearing force on probabilistic collapse analysis of such a structure consisting of the girder with deep web, which results in underestimation of the strength of the girder. (2) In the case of plane frame structure idealized for a transverse ring of a tanker, the probabilities of failure modes with shearing force effect including are very larger than those excluding the effect.