The present invention relates to absorbent articles such as sanitary napkins, panty liners, and incontinence pads. More particularly, the present invention relates to absorbent articles, such as sanitary napkins, that have undergarment covering components (or "side wrapping elements") that automatically wrap 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 at a region therein that is stiffer than the zone of extensibility.