A rocket is placed with its front nozzle directed towards the hole face with the distance between said nozzle and the face being about four diameters of the nozzle exit section. Then the rocket is released, started and the face of the hole is worked by the gas-dynamic jet continuously discharged from the rocket nozzle. The force driving the rocket towards the hole face is somewhat stronger than the reaction force of the gas-dynamic jet and other forces directed contrary to the rocket movement. The broken rock is removed from the hole by the streams of waste gases passing out through the gap between the rocket body and the hole walls. Thus, the hole is sunk by breaking the face with the gas-dynamic jet of the rocket being suspended relative to the hole walls and face.