[en] The vacuum vessel for the Advanced Toroidal Facility (ATF) is a heavily contoured and very complex formed vessel that is specifically designed to allow for maximum plasma volume in a pure stellarator arrangement. The design of the facility incorporates an internal vessel that is closely fitted to the two helical field coils following the winding law theta = 1/6phi. Metallic seals have been incorporated throughout the system to minimize impurities. The vessel has been fabricated utilizing a comprehensive set of tooling fixtures specifically designed for the task of forming 6-mm stainless steel plate to the complex shape. Computer programs were used to develop a series of ribs that essentially form an internal mold of the vessel. Plates were press-formed with multiple compound curves, fitted to the fixture, and joined with full-penetration welds. 7 refs., 8 figs