A surface processing machine employing a processing tape cartridge for polishing or grinding disks or the like. The machine employs a processing tape cartridge which rotatably accommodates in a casing a pair of reels for the winding of processing tape. The machine comprises a cartridge holder for holding the tape cartridge; a tape drawing mechanism to draw out a portion of the processing tape in the cartridge; a guide roller mechanism for setting and transporting the processing tape on a predetermined path of travel; a work holder mechanism adapted to hold and rotate a work at its machining position; and a tape pressing mechanism for pressing the processing tape against the work.