The clamping-support element is a clamping and support element for clamping and supporting workpieces. It has a wedge-shaped self-locking clamping function, double action and a maximum working pressure of 300 bar. The element has the following advantages: one element combines clamping and support functions, wedge-shaped self-locking clamping, hydraulic re-clamping, sudden oil pressure drop, reliable clamping, vibration damping, space-saving embedded cylinder body, arbitrary position installation, interchangeable support screws, and hoses. The element can be used for the following aspects: the workpiece must be firmly clamped even when the hydraulic system pressure drops; the ribs or webs of the workpiece must be clamped and locked in the middle position; the cutting force is relatively high and directly related to the clamping force; the vibration of the workpiece needs to be buffered.