In general the drift result in ship heeling, thus it seems to be necessary to analyze the ship motion by considering both the drifting and heeling phenomena. In this paper, a drift velocity and a heeling angle are given as prior conditions, and then within the linear potential theory the hydrodynamic coefficients and wave exciting forces and moments are derived for a ship advancing and drifting with constant speeds. And numerical calculations are preformed for a cylindrical body of shiplike cross section at zerp forward velocity. The 2-D hydrodynamic forces and moments of a heeled cylinder are calculated by using the Frank Close-Fit method. These numerical results for the oscillating cylinder without drift velocity have shown better agreements with experimental data than the numerical results of Kobayashi[2]. The motion responses for a drifting cylinder are calculated ignoring the drift velocity effect in the free surface condition. The accuracy of these calculations can not be verified, because the experimental data are not available. Through these numerical calculations to so concluded that drift velocity effects on the body motion are signiffcant.