Abstract: The discontinuities of the differential of yield surface to stress components at the corners are caused by the corner singularity of Mohr-Coulomb yield surface,resulting in many problems in the numerical simulation.With regard to these problems,a lot of treating methods are introduced including the smoothness and the non-smoothness methods in the previous studies,in which the non-smoothness disposal methods have been widely applied for their simple implementation.And the studies on their precision have been carried out in many classical cases.But it is not clear that what the rules of the plastic strain are and what the effect of these methods on the plastic strain is.Furthermore,deep researches have not been conducted on how to evaluate the effect quantitatively.So firstly,the flow rules of the plastic shear strain are studied in the frame of the conventional plastic potential theory.Then,the discontinuity phenomenon of the plastic shear strain is discovered in the researches on the rules of the plastic shear strain in which the non-smoothness management is applied.The results of the analysis of this phenomenon indicate that the discontinuity of the plastic shear strain can not be neglected.So,the precision of these different methods should be concretely analyzed in consideration of different cases.