In rotary forging the rocking motion of the upper die results in an instantaneous die contact area which is only a small proportion of the total billet area. Forming forces are thereby reduced to a fraction of the uniaxial forging force. Most analyses developed for force prediction calculate the contact area between the rocking die and the billet without considering the effects of elastic distortion of the dies. In this paper it is shown that elastic distortion results in a substantial increase in contact area and force when cold forging hard metals, particularly when the rocking angle is small. Experimental results taken over a range of test conditions give reasonable correlation with the simple theory. The analysis and experiments are concerned with the upsetting of circular cylindrical billets, but it is considered that the conclusions apply to other component forms.