This paper presents a method for calculating the two-dimensional or the axi-symmetric Oseen flow past an arbitrary body at a finite Reynolds number. An integral equation for the unknown densities of the lifting and dragging Oseenlets distributed on the body surface is transformed into a set of linear simultaneous equations to obtain the solution. In consequence of the present numerical calculations, these results are obtained. (1) “An extended Oseen approximation” is better than the usual Oseen approximation so far as the surface pressure distribution is concerned at high Reynolds number. (2) A pair of standing vortices attaching to the body occur at high Reynolds numbers even in the Oseen flow. (3) The vorticity distribution around a body is very similar to that of the solution of the Navier-Stokes equation.