A disposable absorbent article, such as a diaper, is disclosed. The diaper has two lengthwise extending longitudinal marginal portions, each longitudinal marginal portion having two elastically extensible leg cuffs, a barrier cuff and a gasket cuff. The leg cuffs serve to help contain body exudates within the disposable article. Each leg cuff is elasticized to provide a relatively low ultimate contact force against the skin of the wearer at relatively high elongations. This arrangement provides a diaper with leg cuffs which can be elongated to conform to the shape of the wearer, without causing undue discomfort or irritation to the legs of the wearer. The relatively low ultimate contact force at relatively high elongations may be accomplished either through a low contact force differential material, or through a material which exhibits stress relaxation over a relatively short period of time.