The parallel midbody for the hull of a tanker is fabricated of modules, each made of double-walled longitudinal subassemblies welded to one another and to a bulkhead. The subassemblies are made of outer cylindrically curved plates welded edge to edge, and inner cylindrically curved plates welded edge to edge. Longitudinal rib plates are extended between and are welded into joints between curved plates in the inner and outer hulls. The curved plates are convex towards the exterior of the vessel. At respective transitions between the bottom and sides, the inner and outer hulls have bilge radii which approximate in size the radii of curvature of others of the plates including ones both adjacent to and remote from the bottom-to-side transitions. A fixture for facilitating welding of the T-joints of the subassemblies is provided. The subassemblies and modules are fabricated in an up-ended orientation. Each successively completed module is tilted-over and joined to the growing midbody with the aid of a variable buoyancy barge and a caisson pontoon.