An automatic drilling machine has an electric drilling unit on which a cylindrical cutter is rotatably mounted. The drilling machine includes a drill motor for rotating the cutter and a feed motor for linearly moving the cutter for the purpose of drilling into materials such as concrete. The current flowing through the drill motor before a drilling load is imposed thereon is detected for a microprocessor to determine the type of the cutter being used. The drill motor is driven at a rotation speed suitable for the cutter being used and the feed motor is driven at a speed such that the rotation speed of the drill motor thus set is maintained unchanged. Particularly, the drill motor is driven at a reduced rotation speed from the start of drilling until a predetermined drilling depth is reached to reduce chatter vibration which may otherwise be generated if the drill motor is driven at a regular constant speed from the beginning of drilling until the end.