PURPOSE: To assure an accurate storage by providing, on a clamp device, two clamp jaws for holding a milling shaft at the same axial position as a plurality of the edges of a milling cutter and also the centering surface for a milling shaft.

CONSTITUTION: A clamp device 2 of a milling cutter 1 which has a great many of triangular front edges 3 and 4 and in which a side edge 11 is formed forms a storage part 33 to a chuck 34 in a shaft part 32, forms two clamp jaws 6 for holding a milling shaft 5 at the same axial position as a plurality of edges 3 and 4, and also forms a conical ring-shaped centering surface 37 for supporting an upper end conical surface 38 of the milling shaft 5 at a bottom part having a clamp holding body storing slit-shaped part 35. When a bolt passing through the clamp jaw 6 at a specified angle holds a conical surface 42 of the milling shaft 5, one movement motion of one clamp jaw 6 is transmitted to the other clamp jaw 6 through a ring 48 by the ring 48, and the milling shaft 5 is stored correctly in cooperation with the centering surface 37. Thus the edges of the milling cutter can be set correctly.