The invention concerns a device for machining of work pieces (76) or objects, comprising an elongated tool (10) which rotates about its longitudinal axis and is provided with a shaft (14) which can be coupled to a drive unit (48) and with a chip-removing head (16) connected to the shaft (14). In order to ensure that even a very long tool can be used in deep hollows in the work piece in a stable and vibration-free way, the invention proposes a sleeve (20) between the shaft (14) and the chip-removing head (16), connected at one end to the chip-removing head (16) in such a way that it cannot slide or rotate. The tool can be clamped in the chuck of a hand-held drive unit, preferably with a suction and flushing device (50) connected in series and used to suck away chips through the cavity in the sleeve (20) and to pump cooling fluid onto the cutting site (44).