In this thesis, the upper bound dual stream function elemental technique was used to analyze the forging of spur and helical gears. In this technique, the deformation region is divided into a number of elements in the form of stream-function elements and the stream functions in each region are proposed. The stream function at each point of the element was assumed to be a function of the stream functions at nodes. Numerical calculations have been carried out to compute the total energy consumption, which consists of the energy required to overcome the internal deformation, the frictional resistance between the die and the work-piece and all the discontinuities in the field. This value is a non-linear function of the unknown stream functions, which can be optimized by minimization of the total energy. After the minimization of the unknown stream functions, the lower upper bound of power was obtained, then from the velocity field the nodal point’s movements are determined and the strain values at nodal points are also calculated. By using an interpolation method the strain values at any point can be derived. This method can satisfactorily predict the barreling phenomenon in forming the gear teeth during the deformation and before the die is completely filled. The results obtained from the present investigations consist of the effects of different parameters and are compared to those of the other investigators. Through comparing the results, the validity and reliability of the proposed method were verified.