Things You'll Need
Liquid fabric stabilizer (optional)
Sewing machine (optional)
Like any woven material, elastic will fray. Frayed elastic is unattractive, and fraying can cause the seam to work loose and the whole band of elastic to give way. If the elastic is a hairband, you will only have hair in your face, but if it is a waistband, the results may be much more embarrassing. You can prevent woven elastic from fraying with either a sewn or no-sew method.
Coat the cut ends of the elastic with liquid fabric stabilizer. Liquid fabric stabilizer is available from fabric stores and has a small squirt nozzle, which makes it easy to apply a thin line of stabilizer to a cut edge.
Overcast the ends of the elastic with a machine zigzag stitch. Sew so that one side of the stitch is just beyond the cut end of the elastic.
Prevent fraying when making bands of elastic by overlapping the edges 1/2 inch and sewing a zigzag stitch over the edge of the elastic. Turn the elastic over and sew the overlapping edge on the other side in the same way.
Solid plastic elastic will not fray, but it is not as strong as woven elastic.