An inflatable and deflatable air supported structure which lies flat in its uninflated condition and has a substantially spherical shape in its inflated condition. The structure includes a wall formed from a sheet of flexible material having a first perimeter greatest in its flat condition, the peripheral edge of the perimeter in the inflated condition is rounded in shape and forms a second outer perimeter smaller than the first perimeter. A plurality of cables connected with the sheet extend from the peripheral edge to an inner central portion dividing the sheet into gores between each pair of adjacent cables. The outer ends of the cables extend from beyond the outer peripheral edge to the inner central portion. Two anchorings are provided. One anchoring connects the outer ends of the cables to the ground to connect the peripheral edge to the ground, and the other anchoring connects the cable's inner ends and the central portion to form an air-tight chamber with the flexible material inflated. The other anchoring anchors the central portion to the ground.
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