A clamp device includes a clamp main body, an engagement assembly, a clamp rod, a drive mechanism, and a support mechanism. The engagement assembly can be changed over between a diameter-expanded state in which it engages with an inner circumferential surface of an aperture in a workpiece, and a diameter-reduced state in which it does not so engage. The clamp rod is engaged with an interior of the engagement assembly. The drive mechanism drives the clamp rod to and from the clamp main body. The support mechanism supports the engagement assembly with a pneumatic force of pressurized air. At least a part of the pneumatic force is released after the engagement assembly has been expanded in diameter.