Abstract: A modular unit connection system for joining together a plurality of box-shaped modular units to form a single or multistory building. The modular building units have elongated hollow structural framing members at their vertical corners and four substantially perpendicular vertical side walls extending between their vertical corner members. The side walls are topped with horizontal framing members extending between the vertical corner members. The vertical corner members lie within the planes formed by the side walls of the modular units, and their vertical corner members and their adjacent side walls abut with no significant space between them. The modular units may be connected at their vertical corner members with generally flat connection plates. Threaded tension rods may extend through the hollow vertical corner members and may be coupled to tension rods running through the hollow vertical corner members of vertically aligned modular units.