The invention provides elastic fabrics which are substantially non-extensible in the machine direction and have substantial elastic properties in the cross-machine direction. The process stable fabrics of the invention include a net and a fibrous layer which are secured together. The net is composed of a plurality of continuous machine direction strands and a plurality of cross-direction strands. The machine direction strands are substantially non-extensible and the cross-direction strands are substantially elastic. The fabrics of the invention can be manufactured and processed more readily than fabrics which are elastic in both the machine direction and the cross-machine direction.