To increase the thickness of a lens that can be flat finished without the need for increasing the width of a processing tool.

The eyeglass lens processing apparatus includes: a finishing tool having a bevel groove for beveling and a flat-processing portion; a moving means for moving chuck shafts with respect to a tool rotation shaft in an axis (X) direction and in a Y direction in which the axis-to-axis distance between the tool rotation shaft and the chuck shafts is varied; and a control means for performing flat finishing to the periphery of a lens as subjected to rough processing by controlling the moving means on the basis of a target lens shape and detection results of an edge position detecting means when a flat-processing mode is selected. If the edge thickness is larger than a first threshold, the control means divides a process of the flat-finishing into a plurality of stages, and at each stage, determines a processing position of the lens which has been shifted in the X direction with respect to the flat-processing portion so that an unprocessed portion of the preceding stage is flat-finished on the basis of the front surface edge position and/or a rear surface edge position detected by the edge position detecting means, and making the periphery of the lens subjected to flat finishing by controlling the moving means on the basis of the determined processing positions.