Abstract: A system of sealing containers of plastic material for the sealing of containers having a mouth surrounded by a peripheral flap, consisting of arranging a sealing sheet on the mouth of the container to be sealed, supporting the peripheral flap on a welding mold, and applying ultrasonic vibrations on the sealing sheet, in coincidence with a mold, by means of independent sonotrodes, said mold comprising two concentric walls situated in coincidence with the peripheral flap surrounding the mouth of the container to be sealed, an internal wall allowing for the welding between the sealing sheet and the peripheral flap of the mouth, and another outer wall, of a slightly larger height, finished in an angled edge profile to cause the cutting of the sealing sheet and of said peripheral flap at a certain variable distance from the weld line between said sheet and peripheral flap.