A composite elastic material includes a layer of ribbon-shaped elastomeric elements disposed in machine direction alignment and point bonded to an extensible layer which may be a gatherable layer or a stretchable layer. A layer of meltblown elastomeric fibers may be bonded to the layer of elastomeric ribbon-shaped elements before bonding to the extensible layer. The elastic composite has excellent cohesion, controlled breathability to air and water vapor, an opaque appearance, and is easy to cut and convert to end use products such as garments, pads, diapers, and personal care products where elasticity is desired.