Abstract: Rigorous theoretical analysis of slope stability problems is normally conducted by the upper bound method of plastic limit analysis,considering that the soil material is perfect plastic and obeys the associated flow rule. It’s limitation lies in that the dilatancy obtained from this method exceeds that from experiments. However it will be shown that introduction of the classic non associated flow rule, namely neglecting the volumetric strain completely, neglects the important influence of dilatancy on stability of soil structure.Therefore the general non associated flow rule must be used in order to describe the soil deformation accurately.Based on the condition of plane strain, this paper deduces a D-P yield criterion matching the Mohr Coulomb criterion, which can deal with the effect of angle of dilatancy. The result of an example shows that the discrepancy between the results obtained by FEM based on D-P yield criterion and plastic limit analysis is 3% approximately.It proves that the method provided in this paper is not only reasonable but also can be introduced into current FEM program by transfering the parameter simplely because of the advantages of Drucker Prager criterion.