The most notable aspect of the Lunar and Martian environments is the lack of a substantial atmosphere. Atmospheric pressure on the Moon is essentially zero, and is very low on Mars. Support of human occupancy requires an internal atmosphere and, therefore, the most efficient structure is an inflatable tensile membrane. A generic inflatable module is proposed as an efficient and functional structure for a Lunar/Martian base. Each module consists of thin membranes supported by a framing system composed of cylindrical arches and columns. The framing system maintains the module shape and supports the deflated module. Three options for the framing systems were evaluated. Membrane sleeves filled with structural foam, rigid members made of either titanium or graphite/epoxy composite, and pressurized membrane tubes were evaluated. The pressurized membrane tubes were found to have the lowest mass and be sufficient for supporting the structure. A structural analysis was performed using a three-dimensional (3D) computer simulation. Results from the structural analysis were applied to improve the structural design of the module.