Abstract: The method allows the sealing of metal tubes, particularly of stainless steel, for example, tubes for filling containers for gas at high pressure or evacuation tubes for vacuum vessels. It includes the steps of locally squashing the portion of the tube to be sealed with a pressure capable of achieving the sealed clamping of the tube, freeing part of the squashed portion of the tube, the remaining part being maintained under the clamping pressure, cutting the freed part of the squashed portion of the tube, welding the lips of the part which is still clamped, and finally removing the clamping pressure.