A driving apparatus for a washing machine is disclosed. The driving apparatus includes a tub containing washing water and provided with a drum rotatably installed therein; a double rotor comprising an outer rotor provided with magnets supported by the inner surface thereof, and an inner rotor installed at the inside of the outer rotor and provided with magnets supported by the outer surface thereof; an internal bearing fixed to the rear surface of the tub for rotatably supporting the inner portion of a drum shaft connecting the drum and the double rotor; an external bearing supporter provided with an external bearing for rotatably supporting the outer end of the drum shaft; and a stator fixed to the rear surface of the external hearing supporter so that the stator is disposed between the outer rotor and the inner rotor, and generating magnetic energy for rotating the double rotor by electrical energy supplied from the outside.