To provide a vice device of a bench circular sawing machine and the bench circular sawing machine, superior in compactness and usability, by cutting a cutting object material in a predetermined shape from an oblique upper part, while pressing and holding the thick cutting object material in a small space above a base.

This vice device includes a column 41 provided on the bench circular sawing machine 1 for arranging a body having a saw blade above the base 10 having a guide fence 12 for positioning the cutting object material so as to be vertically movable and tiltable in the lateral direction, erected in the rear of the guide fence and attached with an arm 42, a screw feeding member 43 vertically movable by rotary operation by screwing with the arm in front of the guide fence and a pressing body 45B provided on the lower end of the screw feeding member. The screw feeding member is constituted of a plurality of screw members 44 and 45 connected in the vertical direction Y by coaxially screwing with each other and capable of respectively independently rotary operation, and has the pressing body 45B in the screw member 45 of the lowest position by screwing the screw member 44 of the uppermost position with the arm.