Abstract: A floating chuck having a bush movably mounted on a body is disclosed. The chuck includes a plate having four holes staggered pairwise 90 degrees apart in the periphery of the plate and serving to accommodate four axial fingers, two of the fingers being 180 degrees apart and integral with the body, and the other two fingers being integral with the bush. Each hole has a depth greater than the diameter of the fingers, to allow displacement of the plate in two intersecting directions.The plate includes openings which are regularly distributed and serve to accommodate bearings. The bearings abut two opposed bearing surfaces, one located on the body and other on the bush. The difference between the diameter of bearings and the thickness of the plate is less than the elastic deformation limit value of bearings and the bearing surfaces.