The invention relates to a foldable/deployable structure (1) comprising: —a mast (4) which can be deployed along a longitudinal deployment axis, the mast being designed to be placed either in a folded state requiring little axial installation space, or in a deployed state having a predetermined shape, —a base (10) upon which the deployable mast (4) is rested, the structure (1, 2) further comprising a bracing device, the bracing device: —having at least three points for attachment to the base (10) and at least three points for attachment to the mast (4), the bracing device connecting the base to the mast; —being designed to limit the transverse movements of the mast relative to the base (10) at least when the mast (4) is in a deployed state, and; —comprising at least one connecting member (22, 42, 60) chosen from the group formed by fabrics, non-woven fabrics and ties, the ties being chosen from the group formed by monofilaments, cables, bundles and strips; the structure (1, 2) being characterised in that it comprises a device (30) for tensioning each connecting member of the bracing device when the mast (4) is in the deployed state, the tensioning device (30) enabling a proximal end of the mast (4) to be maintained in the deployed state, at a distance from the base (10) greater than the distance separating the proximal end of the mast (4) from the base (10) when the mast is in the folded state.