A run flat device for use in a wheel assembly comprises a wheel rim made of a plurality of blocks and a tire cover having beads mounted against flanges of the rim. The device includes an annular support structure for mounting around the rim to support the cover, the structure subdivided in at least two ring sectors to form the structure by juxtaposition in the circumferential direction thereof, and means for locking the beads against the flanges to connect the ring sectors to the beads. Each ring sector comprises at least two rigid support elements superposed in the radial direction of the structure and separated in pairs by respective rubber-based resilient layers, the layers adapted to shear based on a lateral force applied to the structure to enable the radially outer support element to be displaced axially relative to the radially inner support element.