Abstract: The modular building system consists of building modules (1) in high resistance, reinforced concrete, to be stacked vertically and placed side-by-side in the construction of preferably residential buildings. Each module (1) forms a monolithic structure or consists of a steel frame (103) and panels (102), with walls, ceiling and floor. These modules (1) include positioning devices (2 and 3) for stacking purposes; side connection elements (5 and 6) between the modules (1); and/or horizontal and vertical tightening bands (104 and 105). These modules are leveled by using leveling sheets and/or non-retraction mortar and/or a method with jacks (108) and tubular sections (109) filled with non-retraction mortar (193) until it sets and the jacks (108) are removed. Each building module (1) includes all the accessories and finishing elements of a home, such as facades, windows, utilities, furniture and interior equipment considered useful.