A modular building system wherein extruded, elongate, plastic building components can quickly, and with no special tools or skills, be snapped and slidably fit together to form a wide variety of different building structures. The proposed system produces frameless buildings wherein surface closure structures, like walls, windows, doors and roof panels are bound into stability through building-wrapping banding structures that include upright, perimeter stabilizer bars, roof trusses, and in most instances, the underlying ground. Within a finished building, the closure structures effectively float and react with relative motion responses to different applied building loads.