Abstract: A head for a pressure vessel has a contoured liner and successive wraps that overlie the liner and conform in contour to it. The liner has a machined outwardly presented surface, whereas the wrap immediately over it has a machined inwardly presented surface, and the liner and wrap are welded together with their opposed machined surfaces in face-to-face contact. The same holds true with the successive wraps so that two adjacent wraps are in face-to-face contact along their machined surfaces. A wrap may be heated prior to being placed over the liner or over another wrap so that upon cooling the wrap shrinks and places the underlying liner and wraps in a state of precompression. Both the liner and the various wraps may be formed from segments which are dished to the proper contour, then welded together into a rough liner or wrap, and finally machined along the appropriate surfaces. They may likewise be formed from single plates, forgings or castings.