A pressure proof reactor vessel and the method of making such vessel wherein the vessel has a cylindrical one-piece outer shell and a cylindrical one-piece cylindrical inner shell, which inner shell has a smooth continuous interior surface spaced radially inwardly from the outer wall and concentric thereto. The outer cylindrical shell is formed from a one-piece material with its radial thickness being substantially greater than the radial thickness of the inner cylindrical shell. Support means in the form of a spiral or vertically disposed is positioned in the space between the cylindrical outer surface wall of the inner shell and the cylindrical outer shell defining a pathway for the flow of coolant between the outer wall and the inner wall. The support means is secured to the inner surface of the one-piece cylindrical outer shell while the inner shell is plug welded to the support means.