An apparatus for welding a covering film superimposed on a sheet of thermoformable plastic material provided with a plurality of containers thermoformed thereupon, includes a first plate arrangement provided with an operating wall for supporting the sheet and a second plate arrangement provided with a welding arrangement for pressing the film and the sheet against the operating wall such as to weld the film and the sheet. The sheet includes a plurality of through holes interposed between the containers, and the first plate arrangement includes a conduit arrangement leading onto the operating wall at the through holes for extracting air from the containers, and/or for directing a gas to the containers.