The three dimensional source distribution method is a popular technic to estimate hydrodynamic pressures on offshore structures during earthquakes. However, because only series-form expression of proper Green function was available, it takes long CPU time for accurate calculation. In this paper, an alternative integral-form expression of Green function is derived and its efficient way to calculation is presented. Resultant acting forces on circular and submerged rectangular cylinders vibrating horizontally under the effective dimensions of cylinders are also presented.