The Magnus force is found by adding the boundary layer displacement surface to the body and then calculating the force on the resulting non- axisymmetric body. The displacement surface is calculated by the simultaneous integration of a differential equation for a streamline, two partial-differential boundary layer integral-momentum equations with the boundary layer thickness and the tangent of the angle between the local direction of the surface friction and potential flow streamline as dependent variables, and a partial differential equation for the displacement surface thickness. The method is applied to a half-ellipsoid of fineness ratio 5 at 4 degrees angle of attack. Slender-body theory is used to calculate the force.