Abstract: An anchoring system and method for fastening a plurality of veneer units (12) to a substrate wall (11) with a waterproof membrane (13) therebetween. The anchoring system (10) comprises a membrane-holding means (14) which is attached to the substrate wall (11) and holds the membrane proximate the wall (11) without puncturing the membrane (13). The anchoring system (10) also includes a support and tie structure (20) including a stationary anchor (19) and a vertically slidable, horizontal tie (24) which is positioned between adjacent units of veneer (12) for stabilization of the veneer wall. The invention further includes means for interconnecting the support and tie structure to the membrane-holding means. In one embodiment of the invention, this interconnecting means comprises a base channel (33) having upper and lower, outwardly extending horizontal legs. The base channel (33) has a central aperture (36) which accommodates the membrane-holding means (14).