The clamping device includes a pair of clamping members arranged in positions to clamp a rib (target portion to be clamped) of a workpiece and having contact surfaces to make contact with the rib; supports configured to support each of the pair of clamping members so as to be able to advance and retreat along a prescribed advancing/retreating direction relative to the rib, and to operate each of the pair of clamping members so as to clamp the rib when advancing; guiding units configured to make each of the pair of clamping members movable in a prescribed positioning direction due to a reaction force occurring when the pair of clamping members clamp the rib; and coil springs (biasing members) configured to elastically bias the pair of clamping members in a direction opposite the positioning direction, thereby capable of positioning the workpiece with high precision without damaging the workpiece.