Abstract: The machine comprises a frame (1) which is secured to the connections (A--A') to which the hydraulic caliper for the brake is usually secured, the caliper having been removed previously. Due to such a connection, the frame (1) will be positioned exactly and firmly with respect to the brake disc, so that by mounting on the frame a grinding equipment comprising the axial feed for the grinding wheel or wheels (15--15'), the disc (D) may be ground without disassembling it. The brake disc is caused to rotate by the grinding wheel working thereon and, optionally, by a small motor-reducer, the arrangement being such as to perform a uniform grinding of the entire surface of the disc. The spindle of the machine, preferably, carries two grinding wheels which, successively, will engage both faces of the brake disc.