Adapters mounted between the beads of a tire and the respective bead seats of a standard rim to permit the mounting of oversize tires on standard rims. A first surface on an adapter is contoured to conform to and engage a respective rim bead seat and flange. A second surface on an adapter is contoured to conform to and engage a respective tire bead. The adapter may comprise an annular body, a pair of cores in the annular body, and a reinforcing ply enveloping the pair of cores.