We have designed the MFTF-B vacuum vessel both to maintain the required vacuum environment and to structurally support the 42 superconducting magnets plus auxiliary internal and external equipment. The design calculations were greatly aided by computer models, which also speeded our redesign effort when the machine configuration was changed to the Axicell MFTF-B this past year. Our field construction and erection effort should meet the July 1984 completion date for the vacuum vessel.