A membrane structure includes an airtight pressure-resistant gasbag and a shape maintaining mechanism which maintains the gasbag in a predetermined shape when the gasbag is in a fully inflated state. The gasbag includes a plurality of spindle-shaped gores of an airtight membrane material, adjacent gores joined together at edges, and a plurality of reinforcing ropes attached to joined sections of the edges, the reinforcing ropes extending along the edges, respectively. Each of the gores outwardly protrudes between two adjacent reinforcing ropes extending along the edges of the gore, respectively, without elongation of the airtight membrane material, when the gasbag is in the fully inflated state. Each protruding gore has a radius of curvature in a direction intersecting the two adjacent reinforcing ropes. The radius of curvature is smaller than a radius of the gasbag.