[en] Several authors have suggested a novel shape for the toroidal field (TF) coils of a tokamak fusion reactor. Collectively, these magnet shapes have become referred to as the ''Princeton D-coil.'' This coil shape can be derived by assuming that for a thin conductor to be in a state of ''pure tension,'' its radius of curvature must be proportional to the toroidal radius. A principal disadvantage of this derivation is that out-of-plane support, a necessary feature in the design of a tokamak fusion reactor, is neglected. A derivation of a bending free toroidal shell for a tokamak fusion reactor is presented. The out-of-plane structure is considered to be an integral part of the fusion reactor and therefore its shape is optimized to produce a bending free stress distribution. This shape, which is nearly circular for aspect ratios greater than 2.5, is derived by solving the equilibrium, constitutive, and kinematic relationships for a uniform toroidal membrane. This membrane is subjected to a magnetic pressure which is inversely proportional to the square of the toroidal radius. A comparison between this bending free shape and the D-shape is presented