Closed die cold forging is an important industrial metal forming process used extensively in the manufacture of headed fasteners. In this paper an upper bound solution is presented based on observed velocity fields resulting from the deformation of initially cylindrical workpieces within hexagonal and square dies. The influence of workpiece aspect ratio, forging loads and friction conditions on the fill-out of the hexagonal and square dies is examined. It is shown that at high die fill-out, friction conditions and workpiece aspect ratio have little influence on the forging pressure ratio. The surface stress state, produced by relative movement between workpiece and punch/die, is examined with the aid of microhardness measurements.