Equipment for grinding external rings of roller bearings includes a supporting pin of a bearing to be ground, a stop extending outwardly from the supporting pin for axial positioning of a side of the bearing, a sliding flange on the pin which can be positioned to rest on the other side of the bearing, a clamping nut which can be firmly positioned on a complementary portion of the pin, skids preloaded by springs situated on opposite sides of the bearing, and a guiding element on the opposite side of the stop, which receives a structure carrying a pair of contrast rolls movable to be engaged with the external ring of the bearing creating a radial force thereon, which can be predetermined and regulated by a maneuvering element to eliminate the clearance of the bearing in the radial direction. A machine for housing equipment of the above specified type.