Within the framework of the Cosserat continuum medium mechanics model, the spherical micro particle is extended and transformed into a square micro particle with consideration of the dipole effect of material points. Based on the Cosserat continuum medium mechanics model, a linear elastic relationship between the couple stress and the curvature strain for the square micro particle is derived, and a generalized yield criterion that can consider the overturning failure of micro particles is put forward. With the finite element analysis program based on the Cosserat continuum medium mechanics model, a numerical simulation was performed in order to analyze the concrete specimens under uniaxial compression and the soil slope stability. The results show that the dipole effect of material points indeed exists, and it is a direct cause of strain localization of materials.