A clamping device for clamping a workpiece having a constant section includes a base a head jaws including a jaw fixed to the base and a jaw facing the other jaw and fixed to the head to clamp the workpiece a guide to link the head to the base and to allow the displacement of the head in an action direction between a clamping position and an opening position. The guide includes at least two plates parallel one with the other with each plate being linked at a first end to a heel of the base and to the head at a second end opposed to the first end, the first ends and second ends being flexible to allow the plates to pivot in relation to the heel and the head, respectively the clamping device being in one block of monolithic material such as metal.
