Among the manufacturing processes, metal forming is commonly used for its minimum material waste and better mechanical properties. Forging is probably the simplest and one of the widely used metal forming process and generally carried out incrementally. Open die forging is the process of deforming a metal in order to shape a product into the given desired configuration. This process is often associated with larger, simpler shaped parts such as shafts, bars, blocks or rings or early stage of closed die forging. In forging operations the prediction of metal flow is an important consideration, since it will greatly influence the formed configuration, mechanical properties of the work piece. The main factors affecting metal flow are friction, yield strength of the metal, and the geometry work piece. During forging of a polygonal block between a pair of flat dies, the material flow developed is non-uniform both in the plane section of the block and along its thickness. The non-uniformity of flow in the plane section is called bulging and that along the thickness of the block as barreling. Both these effects are invariably present during forging of any non-circular block. Analytical solutions are likely to take long time and even sometimes exact solutions may not be found. By using numerical methods, estimations with accuracy and high speed would be made possible by reducing calculation time. In this thesis, a mathematical model for open die forging of regular polygonal blocks using the dual stream functions and also upper bound method has been proposed to examine three-dimensional plastic deformation behaviour of the block between two flat dies. The velocity field derived from the developed dual stream functions can automatically satisfy the incompressibility condition. The non-uniform velocity field was employed for simulating the inhomogeneous deformation and the effect of barreling during the forging. In addition in this study an upper bound solution is developed for forging of such blocks using other velocity field in cylindrical coordinate, taking into account the bulging of sides. Numerical calculations have been carried out to compute the total energy consumption, which consists of the energy required to overcome the internal deformation and the frictional resistance between the die. The upper-bound forging load is determined by minimizing the total power consumption. Using these two models various effects of forming parameter such as the friction factor, reduction, etc upon the non-dimensional forging pressure and barrelling of the blocks. For the sake of illustration, numerical results are given for forging of triangular, square and hexagonal blocks and the results of the velocity field derived from the developed dual stream functions are compared with the results of other velocity field. The theoretical predictions of forging pressure are shown to be in good agreement. The results obtained from the present analysis investigations are compared with the result of the finite element software using Abaqus 6.10 and experimental results. Through the comparison between the results, the validity and reliability of the proposed method was verified. Experiments were conducted using copper alloy and showed to be in good correlation with the theoretical analysis by the dual stream functions. Keywords : Forging, Dual stream functions, Upper bound method, Barreling effect