The object of the invention is to provide a method of polishing the end surfaces of a substrate for a recording medium, which is capable of efficiently polishing the inner peripheral end surface and/or the outer peripheral end surface of the substrate preventing the reliability of performance of the recording medium from being impaired by the adhesion of the residual polishing material. According to the invention, there is provided a method of polishing end surfaces of a substrate for a recording medium wherein an inner peripheral end surface or an outer peripheral end surface of a substrate for a disk-like recording medium having a circular hole at the central portion thereof is brought into contact with a polishing medium obtained by dispersing polishing grains in a viscoelastic resin carrier and the polishing medium flows, thereby to polish the inner peripheral end surface or the outer peripheral end surface.