In a method for the overlay welding of at least one weld layer onto the inner surfaces of pressure vessels made of carbon and low alloy steels as a base metal and used in processes in which hydrogen is contained within the vessels at elevated temperatures and under high pressure, the improvement which comprises welding a first layer weld overlay onto the inner surface of a pressure vessel, consisting essentially of up to 0.1 wt% C, up to 1.0 wt% Si, up to 2.0 wt% Mn, 7 to 12 wt% Ni, 12 to 17 wt% Cr, up to 1.0 wt% Mo, up to 0.1 wt% Al, the balance being Fe, said first layer weld overlay being welded at a welding current within the range of 1000-2800 amperes and at a welding speed varying between 5 to 50 cm/min. so as to produce a weld structure selected from (1) a martensite structure in an amount of 4% to 40% by area in an austenite matrix or (2) a martensite structure in an amount of 4% to 40% by area and a ferrite structure in an amount below 8% by area both within an austenite matrix.