An inflatable structure for gas storage includes an inner bladder containing a gas for storage and an outer wall spaced from the inner bladder. An intermediate space between the bladder and the outer wall is pressurized with a gas (such as air) other than the storage gas so that the structure is protected from environmental conditions such as wind and snow loading. The bladder and outer wall may be flexible fabric membranes and may be provided with lightweight support frames. The structures may be combined in a network of like structures for large scale storage.