A machining head carries at its end a sensor comprising a pressure-sensitive element (4) mounted on the parts (1, 2) holding the injector jet for the machining fluid, as well as the buffering pieces (5, 6, 12) forming a shield. The element (4) is an insulating and watertight tube, arranged to form a ring in the space left between the coaxial, truncated conical surfaces of the parts (1) and (2). It contains conducting parts which come into contact with one another when it is deformed by the action of a pressure whose value exceeds a given threshold. This results in the closing of an electrical circuit which transmits an appropriate signal to the controls of the EDM machine in order to interrupt the relative movement of the head. The device enables any shock or abnormal stress acting on the end of the machining head to be detected. By means of an O-ring seal (7) acting as a hinge, the part (1) and the piece (12) are returned to their original positions when the stress disappears. Also, the seal (7) permits an overrun to occur.