Abstract: A layer head or shell for a pressure vessel is formed by building up successive wraps over a liner, each wrap consisting of a plurality of segments which fit together such that the wrap completely covers the liner or the wrap immediately under it. Each segment is curved to conform to the surface over which it is installed, and once in place a seal is provided along its periphery. Air is evacuated from the space between the wrap segment and the underlying surface so that air at atmospheric pressure will force the wrap segment down tightly against the underlying surface. During this time tack welds are made along the periphery of the wrap segment to join it to the underlying layer. Then the vacuum is released and a final or continuous weld is made along the periphery. As the weld cools it places the underlying layers in a state of precompression.