An omnidirectional wheel including a rim with at least one plate member and a means of attaching the wheel to a vehicle; a plurality of rollers comprising at least two toroidal rows of rollers disposed around the rim for mounting a tire; and a means of actuating the tire around its axis, defined, for example, by the never-ending torus axial member of the tire, whereby, when the wheel is engaging the ground, the tire rolling on the rim causes a side movement of the wheel, parallel to the wheel axis, in a plan orthogonal to the normal plan of rotation of the wheel when attached to the vehicle. A tire having a never-ending torus axial member, a helical bearing member, and a resilient toroidal shape is also provided.