A stackable building wall unit adapted to be stacked with a plurality of identical building wall units in a plane to form a wall comprising three rectangular panels each including inner and outer faces, a pair of spaced apart long edges, and a pair of spaced apart short edges joined to the short edges of the other two panels to form a triangular, stackable building wall unit which can be stacked with the exterior surfaces of the panels in abutting relation. The exterior face of at least one of the panels includes a female recess therein for receiving a complementally formed key to facilitate alignment and preclude relative shifting of the stacked units in a direction extending between said long edges between the long edges. The key may suitably comprise a complementally formed male projection extending outwardly from another panel of an abutting unit. One aspect of the invention contemplates a method of constructing a wall with triangularly shaped building units stacked in a plane with the exterior plane or surfaces in abutting relation. Transverse flanges are provided on the long edges.