Metal forming is one of the most common metal manufacturing processes used, which is noted forrnits minimum waste and dimensional precision, and usually improves the mechanical properties ofrnthe formed part. Metal forming process is a process that causes changes in the shape of solid metalrnparticles via plastic (permanent) deformations. Hence, knowledge of metallurgy and mechanicsrncombine to provide an insight to its behavior. Its applications are wide in the manufacturing ofrnmachinery, automotive, aerospace and other hardware components.rnThe material is modeled as a hyperelastic, viscoplastic solid. A constitutive model with a singlernscalar variable representing the isotropic resistance to the plastic flow is employed. Many finiternelements exhibit the so-called â€˜volumetric lockingâ€™ in the analysis of incompressible or quasiincompressiblernproblems in metal forming. Nearly incompressible plasticity in metal formingrndisplays severe volume locking problems when low order standard nodal-based displacementrnmethods are used. This means that after deformation each small portion of the medium has thernvolume as before the deformation.rnIn this thesis a finite element formulation for a frictionless large deformation contact problem inrnmetal forming is presented. It is based on the formulation which introduces the contact constraintsrnvia Lagrange multipliers. The stabilized formulation which allows the use of low-orderrninterpolation functions for both displacement and the pressure field is applied to eliminaternvolumetric locking effects and to circumvent numerical instabilities. Starting from the variationalrnformulation of the constitutive and the kinematic problems, the linearization of the principle ofrnvirtual work relation, the contact potential energy, and finally the matrix formulation of thernmethod is derived. To improve the convergence property of the method an augmentation step wasrnincluded. Then the formulation is converted to a computer code written using Matlab. Finally thernprogram is used to solve a benchmark example.