Due to complexities of face-hobbing of bevel gears, such as the intricate geometry of the cutting system, multi-axis machine tool kinematic chains, and the variant cutting velocity along the cutting edge, deriving the instantaneous undeformed chip geometry, as one of the most important characteristic of material removal, is a challenging process. In the present research, all these complexities have been taken into consideration to obtain an in-process model and undeformed chip geometry, and predict cutting forces. The instantaneous undeformed chip geometry is obtained using the derived in-process model. As an application of the proposed methods, cutting forces are predicted during face-hobbing by oblique cutting theory using the derived undeformed chip geometry and converting face-hobbing into oblique cutting. The proposed methods are applied on two case studies of face-hobbing of bevel gears and the chip geometry is derived and the cutting forces are predicted.