Under the assumptions of potential theory, small-amplitude motion, small steady disturbance and low current speed, the problem is simplified and then a form of Green function of the simplified equation is derived. For ease of numerical calculation, following the idea of Huijsmans & Hermans (1985), the Green function is expended into an oscillating source Go at zero forward speed and a correction term GI to take into account low forward speed. Then the expressions for Go and GI are derived. It is shown that these expressions have good numerical calculation performance. To test the present method, it is applied to a hemisphere and a half submerged ellipsoid.