A device for the simultaneous double-side grinding of workpiece wafers has two collinear grinding wheels and two hydropads oppositely positioned for hydrostatic bearing of the workpiece, each having at least one hydrostatic bearing and at least one dynamic pressure tube for measuring the spacing between the workpiece and the hydrdopads. The surfaces of the hydropads which face the workpiece are of nonplanar configuration, contoured in such a manner that the spacing between the surface and the workpiece adopts a minimum value near the edge of the hydropads proximate the grinding wheels, this spacing increasing at increasing distance from the grinding wheels. In a further embodiment, at least one bore, through which liquid and abraded material can be discharged from the vicinity of the dynamic pressure tube, is proximate each dynamic pressure tube.