A cuff for placement on the outside surface of a first tube, for example, a tracheostomy or endotracheal tube, and a method of making the cuff. A pattern of the cuff including first and second end regions by which the cuff is to be attached to the first tube is RF welded onto second tube of a thin pliable RF weldable polymer. Polymer material outside the pattern is removed, leaving the length of the cuff including the first and second end regions. The length of the cuff including the first and second end regions is turned inside out to place the cut edge of the weld of the RF welded seam on the inside. The first end region is slipped onto an end of the first tube. The first end region is turned inside out again to orient the cut edge of the weld of the RF welded seam away from the first tube. The first end region is attached to the first tube. The second region is slipped onto the end of the first tube and turned inside out again to orient the cut edge of the weld of the RF welded seam away from the first tube, and attached to the first tube.
