A device for measuring elevations on a surface of a rotary body provided as a cylinder, sleeve, or plate for a graphic industry machine, for instance a flexographic printing plate, includes a first motor rotating the rotary body about an axis of rotation and a measuring device including at least one radiation source, at least one line scan camera, and a computer taking contact-free measurements and combining individual images of the line scan camera to form a joint image. The measuring device preferably includes a reference object such as a wire tautened in an axially parallel direction, a second motor and, if required, a further second motor adjusting the measuring device and/or reference object perpendicular to the axis of rotation. The device provides fast high-precision measurements of elevations such as flexographic printing dots. A system includes the measuring device and a flexographic printing press.