A recessed electrical box with a closeable cover member and at least one outward extending flange. The flange serves as a positioning arrangement to recess the electrical box at the correct depth with respect to the surface in which it will be mounted. The recessed electrical box includes of two pieces, including a one-piece electrical box and a one-piece cover member. An inner flange may be included for positioning the recessed electrical box with respect to the outer surface of the substrate on an unfinished building. The inner flange is removable to facilitate installation on a finished building, in which the finish layer such as siding or stucco is installed. The recessed electrical box may include a second, outer flange, for recessing the box at the correct depth with respect to a wall surface.