In this work, a Stokesian Dynamics simulation, which considers deformation due to induced flows, was performed in order to analyze the behavior of a ring-shaped particle in a Newtonian fluid under shear as well as corresponding rheological properties in the absence of Brownian motion. The following results are obtained: (1) the tumbling orbit is kept when ring is rigid, whereas the normal direction of the ring is the independent of the initial state after a large strain when the ring is flexible. (2) When the ring is flexible, there are two states under shear: a stable state, showing a constant tilt angle, and an unstable state, showing a tumbling motion. (3) When the ring is semi-flexible, in steady-state, i.e., after a large strain, a bi-axial nematic phase is predicted when the system is dilute. (C) 2011 Elsevier B.V. All rights reserved.