Rigid‐viscoplastic finite element equations are used for the analysis of metal forming process. With the view of solution accuracy and computation efficiency, the possible overconstraint of the incompressibility condition is avoided by modifying the penalty method in the variational formulation; and both the direct iterative method and Newton‐Raphson iterative method are combined to solve the finite element equations. The forging process of a ball from a cylindrical workpiece is completely simulated by a remesh procedure. The computed results agree well with the experimental measurements. It is shown, during the early stage of plastic deformation, the effect of friction is small, but gradually increases with further plastic deformation. In the finishing stage, the shear plastic deformation is found mainly in the flash portion. As the shape factor of workpiece increases, the filling of the die cavity is more complete, but the required forming energy increases and the variation of microstructure within the final forged product is intensified. The effect of die velocity also improves die cavity filling.