A deployable and inflatable roof, wall, or other structure has first and second covers made of flexible panels and cables arranged from edge to edge along the covers. Couplings along the edges of the covers connect the structure to supports, such as rails on which the structure can deploy and other supports of a building. Air from blowers blow air in between the covers to inflate the structure like an air cushion. In addition to cables, lateral support for the structure can use struts disposed edge to edge along the covers. Traction or rack and pinion drive mechanisms or cable drive systems can be used to deploy and retract the structure along the rails to cover or open a rooftop or other opening or area of the building.