A resilient wheel has a rim (4) with an airtight annular channel (18) separated from the tire air space (19) by an annular elastomeric member (16). The sealed annular channel (18) is in pressure communication with the tire air space (19) and acts as a buffer absorbing abrupt transient pressure changes produced in the tire air chamber (19).The elastomeric member (16) is seated in depressions (5) in the rim surface stabilizing the beads (6) of the tire mounted on the rim (4). Valve (30) in the rim (4) allows inflation of the annular air chamber (18), providing selective control for the resiliency of the wheel. Continuous radially extending portions (34) of the elastomeric member (16) serve to hold the tire beads (6) in place, the tire beads (6) residing between the extending portions (34) and radially extending portions of the rim structure.