Absorbent articles such as sanitary napkins, panty liners, and incontinence pads are disclosed that have undergarment covering components (or "side wrapping elements") that extend from the main body portion of the absorbent article and automatically fold along the sides of a wearer's panties and provide an alternative to conventional side flaps. The side wrapping elements have at least one zone of extensibility and a region therein that is stiffer and less extensible than the zone of extensibility. The absorbent article preferably comprises at least three regions with different bending moduli to control the location of the absorbent article about which the side wrapping elements will bend.