In the fatigue strength analysis of a ship, it is most important to estimate the accurate stress fluctuation of a certain structural member of the ship in waves. In case the fatigue strength of the structural member is evaluated by the cumulative fatigue damage factor, it is necessary to obtain the long-term probability of occurrence of the stress fluctuation, which is combined with S-N curves. For this purpose, a probabilistic approach is usually adopted, and it is essential to calculate the frequency response function of stress accurately in the probabilistic approach. As for the transverse strength of a ship in waves, hydrodynamic sea pressure in wave is the most important external load, particularly for fatigue strength of a ship. In order to obtain the stress response function caused by the sea pressure, a finite element analysis is necessary to be carried out in every wave condition in principle, because the distribution pattern of sea pressure, as well as the magnitude, along ship' s hull varies according to the wave conditions, and a non-linearity due to the free surface elevation along the side shell plays an important role. However, it may not be possible to conduct this kind of structural analysis in the structural design stage, because it requires enormous time and effort in computation. In the present paper, the stress response function and the long-term probability of occurrence of stress caused by wave pressure are calculated with the use of the most exact method at present. The treatment of the non-linearity due to the free surface elevation along the side shell will be investigated in this process. Then, simplified methods to predict the stress response function and the long-term probability of occurrence of stress are proposed. Comparing these calculated results by the exact method, approximate method and conventional method, the accuracy of the prediction method is discussed from the viewpoint of the design tool for fatigue strength of a ship.