Composite webs having one or more elastic composite structures located on a substrate, methods of manufacturing the composite webs, and articles including the elastic composite structures and substrates are disclosed. The elastic composite structures may preferably include one or more elastic components attached to anchors at two or more locations, wherein the anchors are themselves attached to the substrate. The anchors may preferably be constructed of inelastic polymeric material (and/or exhibit limited to no elasticity in use) and the elastic components may preferably be constructed of elastomeric polymeric material.