The invention provides a modular building unit (1) comprising walls, a floor and a ceiling, which is preferably assembled off-site and furnished or fitted out off-site prior to being transported to a building site for assembly in a stack as a vertical and horizontal array to form a building. The modular building unit is essentially a lined shell defining the walls of a room. Vertical location of one such modular building unit (1) on the unit below it in the stack is established by a downwardly extending location flange (6) around the outside bottom edge of each module, engaging in a peripheral recess (2b, 2c) around the top perimeter of the outside top edge of the vertically adjacent module beneath it in the stack.