A method for cooling an electrical machine includes the following steps: guiding a coolant in an axial coolant supply line which is arranged in the rotor shaft, and conducting the coolant into an interior chamber of the electrical machine via a radial coolant supply line which is connected in a coolant-conducting manner to the axial coolant supply line. The electrical machine has an axial coolant supply line and at least one radial coolant supply line connected in a coolant-conducting manner to the axial coolant supply line, both of which are arranged in the rotor shaft. An interior chamber of the electrical machine is connected in a coolant-guiding manner to the radial coolant supply line.