A flexible container cover with an elastic gathering band around its edge is formed from a rectangular sheet of plastic film with recessed cut corners to form four flaps. The sheet is placed atop a mandrel having a rectangular flat top with eaves or undercut surfaces and four corner slots. Four hooks are positioned outside the slots so they underlie the cut-off corners of the sheet. An elastic band is stretched around the hooks and the flaps of the sheet. The hooks are moved inwardly into the slots to allow the segments of the band to pull and fold a middle portion of each flap inward. A set of tucker blades is then moved inward to push the folded portions of the flaps against side surfaces of the mandrel under the eaves. Four heat-sealing bars are moved up against the eaves to seal the flaps around the segments of the band to form hems.