A corrosion-resistant lath is provided for use in exterior finishing systems, such as stucco systems and exterior insulation and finish systems (“EIFS”). The lath includes in a first embodiment an open, woven fabric comprising weft and warp yarns containing non-metallic fibers, such as glass fibers. A portion of the weft yarns are undulated, resulting in an increased thickness for the fabric. The fabric is coated with a polymeric resin for substantially binding the weft yarns in the undulated condition. This invention also includes methods for making an exterior finish system and building wall including an exterior finish system using such a lath.