The limit state of torsion of ship hulls with large hatch openings is studied. A method to determine the distribution of the plastic shear flow on the hull cross section in the limit state by using the lower-bound theorem is presented together with the corresponding linear programming problem. The limit torsional moment of the hull cross section is obtained based on the distribution of the shear stress in the limit state. Three example limit states for typical containerships of different sizes with large hatch openings are calculated. The calculated limit torsional moments are compared with the design values of wave torque calculated by using the equations given by main classification societies in their rules. A rough estimate of the safety margin is obtained. The results show that for large containerships, it is necessary to pay attention to the safety with respect to torsion. The present method can serve as an effective tool in structural reliability analysis of ships with large hatch openings when the failure mode of torsion is taken into account.