The invention relates to a rotary or fixed cutting tool (1) for machining elements made of a hard and/or abrasive material, said tool comprising at least one active portion having hardness and/or abrasion properties higher than that of the material to be machined, and a passive portion interacting with a tool holder including a clamp (7), characterised in that the active portion (PA) and the passive portion (PP) of said tool are formed by an integral plate defining both portions and obtained directly from a blank having a predetermined constant thickness and a hardness corresponding to that of the active portion (PA) so as to obtain a planar tool, and in that the passive portion (PP) is elongate and has a constant substantially quadrangular cross-section for interaction with a housing (3) with a corresponding cross-section in the clamp (7), wherein the integral planar tool (1) thus formed is directly mounted in the housing (3) secured by tightening the same in the clamp (7).