A structure for fitting around the rim of vehicle wheel and within the tire provides, on deflation of the tire, support for the tire at the ground bearing point and prevents dislocation of the tire beads thus enabling control and reasonable "run-flat" travel to be retained in the event of a puncture. The structure comprises a number of elongate block members (1, 2) which lie transversely across the well (10) in the rim of the wheel (3). The blocks are spaced and retained by reinforced rubber belts (13) and are dimensioned to prevent displacement of the tire beads (11). To enable a tire to be fitted or removed some, at least, of the blocks (1) are in two parts (6, 8) with a pivotal interconnection (15) allowing the center of the block to move away from the rim and the ends to move together thus allowing space for the tire bead to enter the well, this being effected automatically on insertion of a tire lever under the tire bead. Springs (16) ensure the parts of the block return when the tire beads are seated normally. The blocks may include lugs (9) which bear on the base of the well. A majority of blocks (2) need have no pivot.