To provide a clamping device which can fix a work of a simple substance when the work is cut and fit a hand carrying cutting machine attachably/detachably to a prescribed position.

A vice part 2 and a cutting machine fitting mechanism part 4 to which the hand carrying cutting machine 3 can be fitted attachably/detachably are set on a table 1. The handle 22 of the cutting machine 3 is fitted into a through hole 14 in the bracket 8 of the mechanism part 4, and the cap bolt 23 of a hand carrying cutting machine 3 main body is inserted into the engagement recess 15 of the bracket 8, so that the cutting machine 3 can be fitted attachably/detachably on the table 1.