Abstract: A wheel system for securely mounting a tire thereon. The assembly includes a wheel having a rim with radially outward extending slots. A tire with radially inward extending protuberances mates with the radially extending members for securely mounting the tire to the wheel. The mating of protuberances with the members limits radial deflection and rotational movement of the tire about the rim. Axial movement of the tire relative to the rim is limited by the inner surface of the sidewall of the tire abutting the ends of the radially extending slots. In one embodiment, the wheel is composed of material having elastic properties for absorbing shock.