Abstract: A fully automatic bundling machine forms a bundle of stacked compressed rows of rolled tissue product and wraps the bundle with thermoweldable material which is taken from a single roll. For larger rolled products such as household paper towels, the individual product rolls are not upended at any point during bundling, but always remain horizontal. The single roll of thermoweldable material is bundled around a selected number of stacked rows of product after compression thereof, so as to form a tunnel which is open at one end. The compressed product rolls are inserted into the tunnel and the wrapped bundle is advanced to a welding and cutting station which simultaneously closes the open end of the bundle and cuts the thermoweldable material along the weld line such that the wrapped bundle is completely sealed and one end of the thermoweldable wrapping for the next bundle is closed.