A pneumatic runflat tire includes ribs mounted axially outwardly of the carcass ply. The ribs are each made of a non-elastomeric material. The preferred rib is compound composite material having first, second, and third layers. The first and third layers of the rib are a fiberglass and epoxy composite and the second layer is an elastomer. The ribs provide primarily radial stiffness support capability of a sufficient level to support the weight of the vehicle in the absence of tire inflation.