A pneumatic wall structure and a method of making and erecting same. The pneumatic wall structure includes an inner flexible tent sheet, a central flexible tent sheet and an outer flexible tent sheet. The inner, the central and the outer flexible tent sheets are arranged to form a two-layer wall structure comprising (i) an inner layer formed by the inner tent sheet and the central tent sheet and, (ii) an outer layer formed by the central tent sheet and the outer tent sheet. The inner layer is inflatable and provides a main support structure for the wall structure, and the outer layer forms a convection space into which an ambient air is capable of flowing. The inflatable support tubes are arranged between the central tent sheet and the outer tent sheet to provide redundancy to the main support structure and to provide a spacer between the central tent sheet and the outer tent sheet.