A banding machine provides for a controlled intermittent flow of a tubular web or sleeve of thin plastic material from a storage reel, over a tensioning arm and guiding rollers onto a group of machine elements which first open the tube somewhat, stop the flow of material, slice the tube transversely, and pass the cut segment of web over a floating mandrel to form it into the shape of a container positioned below it, while continuing the flow of tubing from the reel down onto the same group of elements to form the next band. The open segment of band is now placed over the container automatically to complete the banding operation.