This paper presents motion analysis of a planar rimless wheel. A spoke that comes in contact with the ground is free to detach from the ground. Detachments may lead to various types of motion such as bouncing. However, previous works usually assumed that the spoke does not detach from the ground until the new spoke impacts with the ground. Then bouncing motions never occur in the simulations. We conducted dynamical analysis of the rimless wheel when the impact is not perfectly inelastic in order to capture bouncing motions. The dynamical analysis clarified the motions of the rimless wheel. When the coefficient of restitution is not 0, the rimless wheel bounces after the impact. The stability analysis demonstrated that the motion of the rimless wheel is stable. Simulation results indicated that the coefficient of restitution affects the walking performance. Copyright (c) 2010 by JSME.