In International Maritime Organization, they decided that an oil tanker newly constructed after 1992 A. D. should have the devices for prevention of oil pollution, and one choice of these devices was to have the double hull. In such an oil tanker, we often adopt more space between longitudinal bulkheads. And the more the heigh tensile steel is used, the heigher the stress level in hull structure will become generally. It is, therefore, expected that the effects of warping in bending upon the stress distribution due to longitudinal bending can not be neglected under the heavy ballast condition in which the rate of change of shearing force becomes large. In this paper, at first, we have carried out some numerical calculations on longitudinal bending stress distributions in the double hull tanker of 140, 300 DWT., applying the method of analysis which has been proposed by the two of us previously. Sea state has been chosen as the regular wave whose wave height equal to 10 metres and wave length equal to the ship's length. After careful consideration, we have following conclusions : (1) The values of normal stresses due to warping in bending come to about from 20% to 30% of those due to bending under the heavy ballast condition. Especially at the gunwale part and/or at the bilge part near in the midship section, it reaches its maximum. (2) Under the hogging condition, the normal stress due to warping in bending is in the same plus/ minus sign of those due to bending at a gunwale/bilge part, within the region where the shearing force is increasing. Under the sagging condition, the situations are reversible. (3) We can regard the ship's hull girder as thin walled constant cross section beam, so far as the longitudinal stress components in the parallel part of ship's hull girder are concerned.