Abstract: A concrete block simulating a Norman brick is formed with two large cores separated by a central web. The cores are adapted to receive insulating foam during manufacturing of the block. Each block is grooved in its opposite ends and recessed in its central web for the reception of wedge elements or keys formed of plastic or the like. Adjacent blocks in each course are interlocked and the courses of walls constructed from the blocks in either a stacked bond or running bond are mechanically interlocked and properly aligned. Epoxy cement is utilized for bonding of courses in a customized wall or in prefabricated panel sections utilizing the interlocking block.