A reversible flange plate for refinishing differently configured brakes on a brake lathe adapter is provided. The reversible flange plate includes a body formed with a hollow bore extending substantially through the center of the body. Opposing rings adjacent the bore are provided for holding a brake during operation of the brake lathe. Opposing lips are provided that extend inwardly from the bore from the peripheral edge of the reversible flange plate, and include a ledge that is engageable with a plane of the brake during operation. In addition, an annular disc is provided with a ledge, between the opposing rings and the opposing lips, for further engagement with a plane of the brake during operation.This abstract is provided to comply with rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure, but this abstract is not to be used to interpret or limit the scope or meaning of any claim.