Parallelepipedic packing containers are made and filled in succession by passing a continuous web of packaging material over a forming device which converts the web into tubular form with an overlapped longitudinal seam. The tube is then filled with the intended contents, e.g., a liquid and is then divided off into individual packing containers by first pressing the tube transversely at longitudinally spaced intervals along broad zones and the opposite sides of the flattened tube are heat-sealed to each other along two narrow sealing regions close to the opposite base lines of the flattened zone while the remaining portions of the flattened zone remain non-sealed. The filled portion of the packing container between successive flattened zones is then reformed into the desired parallelepipedic shape, and the packages are then separated from each other by cutting through the non-sealed portion of the flattened zones thus leaving fins which are then folded down against the opposite side walls of the container to stiffen and reinforce the same. The cutting of the double-walled, non-sealed flattened zone is done quite closely to the narrow sealing regions and in such manner that the fins formed on each package have a single material thickness along substantially the full length of the sealing regions.