To provide a work holder of a fine hole processing apparatus, which can improve the machining accuracy for a V surface edge and the internal diameter of an axial through-hole by carrying out an appropriate rounding operation for the connecting portion of a V surface and the axial through-hole, that is the V surface edge, without enlarging the inside diameter by unnecessarily excessively machining the axial through-hole.

The work holder of the fine hole processing apparatus comprises a first holder 5 having a slurry inlet path 16 provided with an aperture 1 facing the V surface 12 of a workpiece 10, the workpiece 10 having the concave conical V surface 12 and the axial through-hole 11 communicated with the V surface 12, and a second holder 6 having a work holding hole 15, into which the workpiece can be inserted, and a slurry outlet path 17 formed therein. The V surface 12 is separated from the aperture 1 of the slurry inlet path 16 by the distance corresponding to at least the outside diameter d1 of the V surface. In addition, a slurry discharging path 2 is provided between the V surface 12 and the aperture 1 of the slurry inlet path 16.