In view of favorable results from the Tandem Mirror Experiment (TMX) also at LLNL, the MFTF project is now being rescoped into a large tandem mirror configuration (MFTF-B), which is the mainline approach to a mirror fusion reactor. This paper concerns itself with the structural aspects of the design of the vessel. The vessel and its intended functions are described. The major structural design issues, especially those influenced by the analysis, are described. The objectives of the finite element analysis and their realization are discussed at length.