Abstract: Process and apparatus for expansion shaping of at least one localized region in a running portion of the wall of a tube of substantial length, wherein the distance between the expanded region and one of the ends of the tube is to be adjusted with precision; comprising disposing a die around the tube in the region to be shaped, the die comprising an expansion chamber between two cylindrical bearing surfaces, introducing a mandrel into the interior of the tube in the portion thereof which is within the die and delimiting an annular space between the mandrel and the tube, by two sealing regions disposed on respective sides of the expansion chamber at the location of the cylindrical bearing surfaces of the die, introducing a pressure fluid through the mandrel into the annular space, and increasing the pressure of the fluid until the tube becomes deformed against the walls of the expansion chamber.