The toroidal field coil (B-coil) in the Doublet III Tokamak consists of 144 turns, each carrying 195 kA, grouped in 24 bundles of six turns each. The bundles are collectively bonded together near the toroid centerline to form one composite centerpost. The results of the stress analysis of the B-coil show that it is structurally adequate for 100,000 cycles of operation under loading conditions produced by a 40 kG toroidal field. (auth)