A vacuum chamber with an innovative wall structure. Instead of a conventional homogenous wall structure, the invention uses an array of internally-pressurized, thin-walled cells to contain an enclosed volume. The walls are arranged so that when a vacuum is present in the enclosed volume, the cell walls are placed primarily in tension. In this way the likelihood of buckling instability is substantially reduced. The result is a much lighter vessel compared to a conventional homogenous wall vessel of similar strength.