Abstract: A sewing apparatus combines an elastic band with a non-elastic draw cord to form a composite band. The apparatus includes a sewing machine for sewing the draw cord to one surface of the elastic band. The sewing machine forms a plurality of stitches that collectively define a longitudinally extending channel encasing the draw cord. The elastic band is fed through the sewing machine by a set of feed rollers disposed upstream from the sewing machine and a set of draw rollers disposed downstream of the sewing machine. The draw rollers are operated at a higher feed rate than the feed rollers to stretch a segment of the elastic band as it passes through the sewing machine. The draw cord is fed through the sewing machine in side-by-side relationship with the elastic band and is secured to the band while the band is in a stretched condition.