An axial flux machine, in particular a single-sided axial flux motor, for an electrical machining device, has a machine shaft, in particular a motor shaft, a disc-shaped stator, a disc-shaped rotor which is arranged adjacent to the stator in the axial direction of the machine shaft. The stator is formed as a winding carrier for at least one stator winding and the rotor, which is connected to the machine shaft in a rotationally fixed manner, can be set in a rotational movement relative to the stator, and with a housing for receiving the stator and the rotor. A first bearing, in particular a fixed bearing, is integrated directly into the winding support and/or into a first stator yoke for mounting the machine shaft. An electrical processing device with an axial flux machine is also disclosed.