Abstract: A wheel assembly incorporating a solid tire having a controlled deflection under load. A wheel assembly (20,200) includes a solid tire (22,202) mounted on a rim (24,204). The rim includes a plurality of axial grooves (68), radial grooves (60), or "U" shaped slots (216), which engage the sides and inner circumferential surface of the solid tire to prevent its slipping around the rim when applying a tractional force. In addition, the outer circumference of the rim includes ridges (50) or radial projections (224) between which are disposed depressions into which the solid tire may deform when subjected to a radial load. The volume provided in the depressions around the outer circumference of the rim and the shore hardness of the composition from which the solid tire is made determine the extent of radial deflection of the solid tire as a function of load so that it is within a required range.