A lightweight “inflatable” tensioned-membrane-structure vacuum container is proposed and its stability is analyzed. The proposed structure consists of a pressurized lobed cylindrical “wall” surrounding a central evacuated space. Stability is analyzed by discretizing the system and diagonalizing the second derivative of the potential energy. The structure is found to be stable when the pressure in the wall is greater than a critical pressure. When membranes are nonelastic, the critical pressure is found to be greater than the pressure required for equilibrium by a factor of . When membranes have only finite stiffness, a first-order correction to the critical pressure is found. Preliminary experimental data show that a stable structure can be made in this way, and that the observed critical pressure is consistent with theory. It is also found that such structures can be designed to have net positive buoyancy in air.