Abstract: A multistory building is constructed by positioning in spaced-apart relationship on a concrete base a plurality of box-like room units each having parallel ceiling and floor panels joined by a continuous perimetric side wall. The room units are bolted to the base and partition panels are positioned in upright position between the room units to subdivide the regions between these room units into horizontally separated room spaces. Floor panels are then bridged between the room units over at least some of the room spaces and the floor panels and partition panels are all bolted in place onto the room units and each other. Thereafter second-floor room units are bolted on top of the first-floor room units along with further partition and floor panels so as to form a second floor and the building is constructed upwardly for as many floors as desired in this manner.