Based on the constitutive relation in crystal plasticity,anisotropy of cyclic hardening of meso-plastic deformation flow and nonlinear movement of crystal slip was considered.Using the Voronoi polycrystalline as a representative volume element (RVE),the mesoscopic mechanical constitutive relation of nickel based polycrystalline superalloy was described by the theory of crystal plasticity.Calculations of both symmetric and asymmetric cycle analyses were conducted.The results of symmetric cyclic analyses indicate that the model is suitable to simulate the strain hardening phenomenon and Bauschinger effect.The results of asymmetric cycle analyses show that the model has the ability to describe ratchet behavior,back stress calculations have great impact on the evolution of slip shear strain rate,slip shear strain rate value largely depends on nonlinear evolution led by back stress hardening process.