Incompressible viscous flows around a three-dimensional ring at Re=50 where the ring axis is parallel and vertical to the free stream have been numerically investigated. A Navier-Stokes equation solver employing an overset grid system was applied to treat the complex geometry. The following things were elucidated. When the ring axis is parallel to the free stream, the pressure on the ring axis obeys a similarity relation. The minimum pressure on the axis occurs just beyond the throat of the ring. The stagnation point exists in the inner side of the ring. The aerodynamic force in the ring plane directs outwards. This force and the drag coefficient decrease as to a smaller ring radius. When the ring axis is vertical to the free stream, the flow patterns were clarified for both the stationary and the rotating cases. To compare the two cases, the stagnation point moves in the direction opposite to the rotation. The stagnation pressure and the pressure in the rear part of a rotating ring are lower than in the stationary case due to the centrifugal force. Lift occurs in the rotating ring and the drag coefficient is slightly larger than that in the stationary case. Both lift and drag coefficients are smaller than in the two dimensional case.