A modular building unit (1-6, 1A) including a building block (10, 10A) having lower and upper faces (9, 9A, 11, 11A), side faces (12, 12A, 13, 13A) and end faces (14, 14A). At least the lower and upper faces are provided with mounting strips (21-24, 53A, 54A) interfit with mating mounting strips (21-24, 53A, 54A) on similar adjacent modular building units (1-6, 1A) to join the adjoining building block units (1-6, 1A) in predetermined dimensionally accurate relationships. A method of securing the mounting strips (21-24, 53A, 54A) to the building block or brick (10, 10A) and the method of interlocking and securing adjacent modular building units (1-6, 1A) to each other are disclosed. A preferred embodiment of mounting strips (53A, 54A) is shown in FIGS. 8-10. A mold (203) is shown in FIG. 12 for the preferred method of forming a building block or brick (200).