A method of making an elastic composite web from which elastic composite bodies of an absorbent article may be separated, the method comprising: conveying a continuous web of material sheet (212, 213) in a longitudinal or machine direction; applying multiple continuous distributions of elastics (210, 211) onto the moving web to form a web of elastic composite, whereby the elastic distributions generally extend in the machine direction; periodically applying a core section on the moving elastic composite web; and continuously applying a top material sheet onto the web including the core sections; wherein applying the multiple continuous distributions of elastics includes applying a first set of elastic strands along a top edge of the moving web, applying a second set of elastic strands along a bottom edge of the moving web, and applying first and second inward sets of elastic strands (211a, 211b) inward of the first and second sets elastic strands; periodically varying the lateral position of the inward sets of elastic strands, relative to the machine direction of the moving web, as the inward elastic sets are advanced in the machine direction toward the moving web of elastic composite to establish first and second periodic, curvilinear patterns of distributions of elastics on the moving web of elastic composite; whereby alternating regions are formed including a first region wherein elastics of the first periodic, curvilinear pattern of distribution of elastics are spaced apart at a maximum distance from elastics of the second periodic, curvilinear pattern of distribution of elastics, and a second region wherein elastics of the first periodic, curvilinear pattern of distribution of elastics are positioned closer to the elastics of the second periodic, curvilinear pattern of distribution of elastics than in the first region; and wherein periodically applying the core section onto the moving elastic composite web includes placing the core section onto the elastics on the moving web, whereby said elastics of each set of elastic strands traverse continuously across the moving web whereabout said core section is placed. conveying a continuous web of material sheet (212, 213) in a longitudinal or machine direction; applying multiple continuous distributions of elastics (210, 211) onto the moving web to form a web of elastic composite, whereby the elastic distributions generally extend in the machine direction; periodically applying a core section on the moving elastic composite web; and continuously applying a top material sheet onto the web including the core sections; wherein applying the multiple continuous distributions of elastics includes applying a first set of elastic strands along a top edge of the moving web, applying a second set of elastic strands along a bottom edge of the moving web, and applying first and second inward sets of elastic strands (211a, 211b) inward of the first and second sets elastic strands; periodically varying the lateral position of the inward sets of elastic strands, relative to the machine direction of the moving web, as the inward elastic sets are advanced in the machine direction toward the moving web of elastic composite to establish first and second periodic, curvilinear patterns of distributions of elastics on the moving web of elastic composite; whereby alternating regions are formed including a first region wherein elastics of the first periodic, curvilinear pattern of distribution of elastics are spaced apart at a maximum distance from elastics of the second periodic, curvilinear pattern of distribution of elastics, and a second region wherein elastics of the first periodic, curvilinear pattern of distribution of elastics are positioned closer to the elastics of the second periodic, curvilinear pattern of distribution of elastics than in the first region; and wherein periodically applying the core section onto the moving elastic composite web includes placing the core section onto the elastics on the moving web, whereby said elastics of each set of elastic strands traverse continuously across the moving web whereabout said core section is placed.