The dowel hole drilling machine comprises a workpiece support. One part of the workpiece support and a crosspiece carrying the drilling unit are mounted to be pivotally movable in unison about an axis. That workpiece support comprises eccentrically mounted supports, which are adapted to be aligned and flush with the workpiece support and to protrude beyond a workpiece support, which extends at right angles to the workpiece support and is spaced the same distance from the pivotal axis as the workpiece support. The workpiece support serves to support the workpiece during a horizontal drilling operation. When the drilling unit is in a vertical position, the stops are flush with the workpiece support and serve as stops for the drilling of the first row of dowel holes. This results in an exact coordination of the drill and the workpiece support, which constitutes a stop for and defines the location of the reference edge during the horizontal and vertical drilling operations. That coordination will not be changed by the pivotal movement of the drilling unit.