An abrading machine with a workpiece support surface on which flat workpieces are transportable in a transport direction (A) through the abrading machine, a circulating abrading belt parallel to the transport direction, and a presser bar extending transversely to the transport direction across the width of the abrading belt with a plurality of presser elements which by way of a control unit are controllable independently of one another, having an apparatus for optically determining the surface contour of flat workpieces in a wide belt abrading machine, characterized by an elongated bar shaped housing which contains an optical sensing apparatus with at least one light source for creating a sensing beam and a deflecting device which moves the sensing beam back and forth between the longitudinal ends of the housing, and in that in one of its side walls the housing has an output window extending longitudinally of the housing for the sensing beam and an input window parallel to the output window for the sensing beam as reflected from the workpiece or from the workpiece support surface, with a row shaped light receiving arrangement being located behind the input window within the housing and having a plurality of optical sensors, the output signals of which sensors are transmittable to an evaluation unit, with the bar shaped housing upstream of the abrading belt extending transversely of the transport direction across the workpiece support surface with the output window and the input window turned toward the workpiece support surface, and with the evaluation unit being connected to the control unit.