A tubular bagging machine includes an innovative indentation-forming device and a modified cross-sealing device. The innovative indentation-forming device includes two punches that form two indentations in the foil web. The machine then forms the foil web into a foil tube with the indentations aligned directly opposite each other and bowed outward. The cross-sealing device includes two opposing sealing jaws each having a blank formed in it. The jaws are closed together to form transverse seal zones in the foil tube. The blanks are aligned with each other and receive the aligned indentations so that they are not sealed together, resulting in the formation of an air bubble in one of the seal zones. Also disclosed are methods of manufacturing the bags, bags produced by the disclosed machines and methods, and retrofit kits for upgrading existing tubular bagging machines.