An elastic composite is formed by securing an elastic member to a substrate along a securement path extending longitudinally of the substrate. The position of the elastic member on the substrate varies laterally along the longitudinally extending securement path in a generally periodic wave pattern having at least one period within the securement path. The periodic wave pattern is such that the elastic composite is more stretchable in the direction of the securement path than transverse to the securement path. In another embodiment, the securement path varies laterally as it extends longitudinally along the securement path. The position of the elastic member varies transversely within the securement path to at least partially define a width of the securement path.