An ostomy belt has an elastic support membrane with a fibrous surface and an aperture for accessing a stoma. The aperture is formed by the user in a preferred location, and the area around the aperture is stabilized against stretch by applying a patch of relatively inelastic hook material to the fibrous surface about the aperture. An elastic membrane of an adhesive bandage is similarly stabilized about an opening in the bandage, by a hook patch that may have a flap for securing an IV tube.