An elongate elastic member is secured to a substrate to form an elastic composite. The elastic member extends along an elastic axis between a first location on the substrate and a second location on the substrate spaced longitudinally from the first location. At least a portion of the elastic axis is generally non-parallel to the longitudinal axis of the substrate. The elastic member crosses its elastic axis at least twice as it extends along the elastic axis, with the elastic member crossing itself at least once as it extends along the elastic axis. In another embodiment, the elastic member generally forms a wave pattern which defines a width of the securement path and has at least two different periods along the securement path. In yet another embodiment, the elastic member defines a continuous series of loops wherein each loop defines a closed portion having a generally tear-drop shape.