A linear numerical method to simulate time varying internal pressure of fluid cargo induced by ship motion is presented. The objective of this study is to develop a part of total system by which the safety of the ship structure may be evaluated. Two dimensional problems are solved by finite element techniques while the boundary element method is applied to the problem of three dimensional tank.The effect of small free surface in the air pipe of the full loaded tank is investigated. Special attention is paid to the case where the tank is fully loaded but has no free surface. In this case it is found that the hydrodynamic pressure fluctuation due to heave or sway motion is zero at the gravity center of internal fluid in the tank.