A two-dimensional rimless wheel provides a simple model of bipedal walking. The motion of the rimless wheel is stable, and this particular property has clarified the fundamental role of a swing leg in planar bipedal walking that addresses the problem of falling forward. In this paper, a three-dimensional rimless wheel is investigated as a simple model of three-dimensional bipedal walking. The 3D rimless wheel model is useful in understanding the essential dynamics of 3D bipedal locomotion. The model consists of two rimless wheels connected by a link at the center of the wheels, and flat feet connected to the spokes with springs. The first numerical stability studies indicated that the motion of the 3D rimless wheel could be unstable; however, numerical simulations and experimental results showed that for a given slope and physical parameters, including the spring constant at the ankles, a stable motion is obtained. This indicates the usefulness of ankle springs in providing stable bipedal locomotion in three-dimensions.