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.