A method for producing elasticized composite side panels (16) and non-elasticized side panels (18), comprising: - feeding a continuous web of a first non-extensible material (46) having longitudinal side edges along a first direction parallel to a longitudinal axis of said web (46), - forming in said web (46), in a position within said longitudinal edges, and at a pitch (PI), a plurality of oblong openings (52) having a major axis substantially parallel to the longitudinal axis of said web (46), each opening (52) having a maximum transverse dimension with a first length (1), a maximum longitudinal dimension with a second length (L), and two longitudinal end zones, - forming a plurality of rectangular elements (68) of elastic material having - in a relaxed condition - two minor sides (68') with a first dimension (d) greater than said first length (1) and two major sides (68") with a second dimension (D) at least equal to said second length (L) of said oblong openings (52), said elements of elastic material (68) being elastically extensible at least along the first dimension (d), - transferring each of said rectangular elements (68) of elastic material - in a relaxed condition - onto said continuous web (46) at each oblong opening (52) and in a substantially centered position with respect thereto, - welding each rectangular element (68) to said continuous web (46) along at least the respective longitudinal edges superimposed on the longitudinal edges of each oblong opening (52), so as to form a continuous composite web (46'), - making transverse cuts (82, 82a, 82b, 82') at predetermined intervals on said continuous composite web (46') so as to remove transverse portions (84, 84', 184) from said continuous composite web (46') comprising the longitudinal end zones of each oblong opening (52) and the corresponding minor sides (68') of each respective rectangular element (68) of elastic material, to form - alternately - individual elasticized composite panels
