I am cutting up two fitted sheets at present. One the elastic was not stretching at all it would have teen easy to remove as it was not sewn to the fabric at all. However I wanted to use the fabric for VBS costumes so just cut the elastic off. The other sheet the elastic ( similar to lingerie panty leg elastic} was sewn inside the turn over at the edge so I cut it off. But you could just replace the ends with elastic and it should stay on