PURPOSE: To enable a work having any configuration to be clamped, by providing hydraulic chucks for pressing that is opposed to a stationary stopper and whose position can be adjusted, in an apparatus for clamping a longitudinally tapered work.

CONSTITUTION: A slidable rail 2 is provided which can rotate on a work table 1 and around a hole 32'. The hydraulic chucks 3, 3 and clampers 4 are provided slidably on the slidable rail 2. Rear face securing stoppers 5 are arranged opposite to the hydraulic chucks 3, 3 and the clampers 4, and side face securing stoppers 6 are fixed laterally of the work table 1. Each of the hydraulic chucks 3 has a cylinder section 24, and a work abutting section 7, and the work abutting section 7 can be pivoted on a pin 8, and has an elastic material 9 mounted to its tip.