Abstract: A building construction for fabricating a veneer, facing wall on a building wall. The construction includes a flat panel of thin rigid material that is adapted to be secured to the building wall. The panel has a plurality of spaced parallel ridges which form flat-bottomed troughs therebetween. Veneer building blocks are held in the troughs by use of adhesive and these blocks may be spaced and staggered to provide the appearance of a conventional brick wall. Crosspieces are held in the troughs between adjoining ends of adjacent blocks. The ridges and crosspieces have exposed surfaces to provide the appearance of mortar between the veneer blocks.