A cup attaching apparatus for attaching a cup as a processing jig to an eyeglass lens including an illumination optical system including an illumination light source arranged to illuminate a side of the front surface of the lens by light from the light source; an imaging optical system including an imaging device and a retroreflection member placed on an opposite side from the light source with respect to the lens; an image processing device adapted to process an image signal from the imaging device to detect at least one of a mark point provided on a unifocal lens, a small lens portion of a bifocal lens, and a progressive mark provided on a progressive focal lens and obtain a position of the detected one; and an arithmetic control device adapted to determine an attaching position of the cup based on the position obtained by the image processing device.