A clamp device has a grip member for gripping the inner peripheral surface of a hole in a workpiece, a clamp rod having a tapered shaft portion that is fitted into and engaged with the grip member, a hydraulic cylinder for driving the grip member and the clamp rod forwards and backwards in the axial direction, and a main body member to which the above elements are mounted. A tubular cylindrical main body portion projecting upwards is provided at the center portion of an upper half portion of the main body member. The outer diameter of this tubular main body portion is set less than or equal to three times the outer diameter of the grip member in the unclamped state, and, in the unclamped state, the upper half portions of the grip member and the tapered shaft portion are made to project outward from the upper end of the tubular main body portion.