The milling tool (1) has a spindle (2, 3), which is mounted in a housing (8) and carries a milling head (14) fitted with cutting inserts (15). Arranged in the drive train of the milling head (14) is a torque-transmitting resilient coupling (13). The spindle (2, 3) actually comprises spindle parts (2, 3) that are connected by a plug-in connection via a bearing bush (9, 10) and can be turned with respect to each other, and the coupling (13) is arranged between these spindle parts. The resilient coupling comprises a helical spring (13) that is fastened by each of its ends to a spindle part (2, 3). The milling head (14) is fitted with sharp-edged cutting inserts (15), which have a wedge angle of 40-75° and have on the milling head (14) a position in which they operate with a positive rake angle of at least 6° and a clearance angle of at least 6°.