This paper is concerned with -the numerical a-nalysis on the secondary flow between two concentric torus-shaped curved pipe with the change in III which is the ratio between the radii of the inner and outer periphery circles. The primary and the secondary flows are solved by a method of series expansion, based on the momentum equation for the flow fields. The first term of the series expansion is determined and the analytical and graphical expression is presented for the secondary flow. It is known that the boundary layer exists, at which the directions of the secondary flow stream lines are reversed, but this study confirmed that the secondary flows are reduced with the increase of the