In the first part of this research, we focus on improving the recently introduced volumetric-forces-method while addressing the possibility of confronting instability in the solution of two dimensional plane strain elastic problems with incompressibility behavior. The method is based on an iterative procedure for elimination of displacement modes responsible for volume change, i.e. in each step a series of forces which cause volume change in the elements are evaluated and adversely applied to the system to remove the modes. This is performed by considering an artificial compressibility to the original problem. Since the well-known Babu?ka-Brezzi condition is not satisfied while using linear triangular elements (locking effect may be seen in the solution), one must employ a series of suitable control volumes in place of the original elements in order to calculate the forces. As this method does not apply constant volume condition directly on the elements, its results do not show locking effect. In this part of the thesis, a new approach has been proposed for defining the control volumes so that the final solution shows stability and convergence after a large number of iterations. This paves the way for the use of the method in nonlinear plastic problems. In the second part, we consider the extension of the aforementioned method to 2D plane strain problems with elasto-plastic material behavior obeying von Misses yield criterion. In this way, the method is employed to eliminate displacement modes responsible for plastic volume change while considering an artificial volumetric plastic strains in the process of the numerical plastic solution, i.e. in each equilibrium Newton- Raphson iteration the modes which produce plastic volume change in the control volumes are removed. To this end some simple amendments are proposed to the well-known numerical plasticity routines. The method has been tested on some benchmark problems and excellent results have been obtained.