Abstract: Apparatus is disclosed for threading tapping holes in workpieces wherein the tapping hole is surrounded by a surface having alternating recesses and arcuate projections which are to be threaded. The apparatus has a hold-down plate one side of which is movable against the exposed side of the workpiece, a carrier which is reciprocable toward and away from the workpiece by a plunger and a spring, a tool holder which has external threads meshing with the internal threads of a nut in the hold-down plate and a helical cam groove receiving a pin of the carrier, and a fluted tap which is coaxially affixed to the holder and extends into the tapping hole when the hold-down plate abuts against the workpiece whereby the externally threaded ribs of the tap which alternate with the flutes extend into the recesses in the surface surrounding the tapping hole.