An absorbent sanitary article comprising: - a chassis having a longitudinal axis, a front and a rear waist section (16, 18), and a crotch section intermediate between the front and rear waist section (16, 18), the chassis including a topsheet having an outer surface which in use is in contact with the user's skin, a backsheet, and an absorbent core disposed between the topsheet and the backsheet, - a pair of elastic leg cuffs extending at least in part along directions parallel to said longitudinal axis and attached to said outer surface of the topsheet, - at least one gasketing element having a longitudinal axis oriented in a transverse direction orthogonal to said longitudinal axis, wherein the at least one gasketing element has a length in the transverse direction which is less than the length in the transverse direction of the chassis, wherein the at least one gasketing element is attached to said outer surface of the topsheet in at least one of said front and a rear waist section (16, 18), wherein said at least one gasketing element is not stretched in said transverse direction and has two opposite lateral portions overlapped and fixed to elastic end portions of said elastic leg cuffs, a central outer portion extending between said two opposite lateral portions and fixed to the outer surface of the topsheet and a central inner portion extending between said two opposite lateral portions and detached from the outer surface of the topsheet, wherein said central inner portion of the gasketing element is raised from the outer surface of the topsheet and forms a pocket open toward said crotch section, characterized in that said at least one gasketing element is made of a non-elastic material, and that said two opposite lateral portions of the gasketing element extend partially on non-elastic end portions (44, 46) and partially on elastic end portions of the elastic leg cuffs. - a chassis having a longitudinal axis, a front and a rear waist section (16, 18), and a crotch section intermediate between the front and rear waist section (16, 18), the chassis including a topsheet having an outer surface which in use is in contact with the user's skin, a backsheet, and an absorbent core disposed between the topsheet and the backsheet, - a pair of elastic leg cuffs extending at least in part along directions parallel to said longitudinal axis and attached to said outer surface of the topsheet, - at least one gasketing element having a longitudinal axis oriented in a transverse direction orthogonal to said longitudinal axis, wherein the at least one gasketing element has a length in the transverse direction which is less than the length in the transverse direction of the chassis, wherein the at least one gasketing element is attached to said outer surface of the topsheet in at least one of said front and a rear waist section (16, 18), wherein said at least one gasketing element is not stretched in said transverse direction and has two opposite lateral portions overlapped and fixed to elastic end portions of said elastic leg cuffs, a central outer portion extending between said two opposite lateral portions and fixed to the outer surface of the topsheet and a central inner portion extending between said two opposite lateral portions and detached from the outer surface of the topsheet, wherein said central inner portion of the gasketing element is raised from the outer surface of the topsheet and forms a pocket open toward said crotch section,