The use of highly efficient constitutive equations improves the prediction of physical phenomena occur during the simulation of metal forming processes. Plastic flow localization and micro-defects growth, which is called ductile damage and occurs during metal forming proccesses, has made the use of advanced constitutive equations which count damage unavoidable. In this thesis, a computational anisotropic ductile damage model, which has high potential to predict damage, is implemented. Firstly, the constitutive equations are introduced and a non-associative elasto-plastic model which includes nonlinear isotropic and kinematic hardenings is presented. The “Hill” quadratic equivalent stress norm is used to describe large plastic anisotropic flow, and a symmetric second-rank tensor is used to describe anisotropic damage state variable. Following the concept of effective state variables, total energy equivalence assumption and a symmetrized fourth-rank damage-effect tensor are used to apply anisotropic damage variable in the constitutive equations. econdly, the numerical integration of the fully coupled anisotropic constitutive equations is performed using a fully implicit incremental integration together with an asymptotic integration scheme and a return mapping algorithm is used for the implementation of anisotropic damage model. A system of nonlinear equations has to be solved in the return mapping algorithm. The system of nonlinear equations contains an algebraic equation and two tensor equations. Each of the tensor equations is converted into six algebraic equations and therefore there are thirteen equations to be solved iteratively. The iterative secant method is used for solving the system of nonlinear equations. Two different techniques are presented to solve the nonlinear equations by the secant method. In the first one, the whole thirteen coupled equations are solved by the secant method. Since one of the tensor equations has a high degree of nonlinearity, the first technique needs a lot of iterations to get a convergent solution. The second technique is introduced to improve the convergence rate. In the second technique, thirteen equations are reduced to only seven equations and six equations are decoupled. The simulation results of these two techniques are compared and it is concluded that the second technique increases significantly the computational efficiency by accelerating the convergence rate while introducing a reasonably small error. Next for the implementation of anisotropic damage model in the commercial finite element software ABAQUS, a user defined subroutine VUMAT is developed. Then, anisotropic damage growth under simple tensile, cyclic and shear loadings are discussed and isotropic and anisotropic damage are compared based on their effect on elasticity. Finally, a square-cup deep drawing process of a steel sheet is simulated by the implemented anisotropic damage model. ABAQUS/EXPLICIT finite element software is used for the simulation of this process so that critical damage zones are identified. After analyzing square-cup deep drawing process by the developed model, the outer surfaces of square box corners are predicted as crack initiation zones. The predicted failure areas by the anisotropic damage model are in good agreement with experimental results qualitatively and this indicates the capability of the anisotropic damage model for damage prediction of metal forming processes. Keywords: Constitutive equations, Anisotropic ductile damage, Elasto-plastic model, Deep drawing process