To provide a cutter vice unit with its front vices securely clamping work such as polygonal lumber even if the lumber to be worked on has an extensive bend (rugged surface).

A vice unit provided here comprises a movable reference-side front vice 11 having a vice jaw 17 and a moving-side front vice 13 provided with a vice jaw 19 which approaches to and retreats from the reference-side front vice 11. This vice unit is characterized in that the two vice jaws 17 and 19 are installed on a horizontal plane through the intermediary of hinge members 21 and 13 to rock relative to the reference-side front vice 11 and moving-side front vice 13.