Disclosed is an apparatus for mounting workpieces to be measured, in particular sheet metal parts of a vehicle body, in a reference position, comprising a plurality of mounts each of which has a support column and can be moved on a support surface into a desired position, and further comprising connecting devices which can be fixed to the support columns and comprise an element for connecting to a support head which rests against the workpiece and is disposed in accordance with the desired position. The connecting element can be adjusted while compensating for deviation of the mount from the desired position.