A method is described for making an elasticized absorbent article having a waist opening and a pair of leg openings. First, multiple distributions of elastics are applied on a moving material sheet to form a moving web of an elastic composite. Then, each of a core section and a second material sheet is periodically applied onto the moving web to define a finished web of discrete elastic composite bodies. In subsequent steps, discrete absorbent pants articles are shaped from the finished web.