The ultimate strength of a ship’s hull depends on its material and geometric properties, some or all of which may be random in nature. In addition, initial imperfections in the form of initial deflection and residual welding stresses in plating between stiffeners can significantly affect the hull ultimate strength. In this paper, the effect of randomness in yield strength and in the initial imperfections on ultimate hull girder strength is determined. Different levels of statistical dependence between yield strength and initial imperfection of stiffeners and plating between stiffeners have been considered. The methodology is applied on a bulk carrier and a VLCC tanker.