In this paper，a new bicrystal model, consists of primary and stray grains, is proposed to simulate the weakening effect of stray strains generated at geometric discontinuities of single crystal (SC) superalloy. A constitutive model considered crystallographic orientations is introduced, and then the bicrystal model under uniaxial loading is built and analyzed in commercial finite element software ABAQUS. The numerical simulation results indicate that yield strength and elastic modulus of stray grains, which can be determined by the crystallographic orientation, have a significant effect on the deformation of the bicrystal model. To evaluate the local stress rise at the sub-boundary of primary and stray grains, a critical stress based on the yield criterion of SC material is proposed. In the elastic stage, as the elastic modulus difference between primary and stray grains increases, the local stress rise would be more severe. In the elastic-plastic stage II, while the yield strength of primary grains is greater than that of stray grains, the lower the yield strength of stray grains is, the smaller load the bicrystal structure can sustain. Finally an evolution equation of critical stress is constructed with consideration of stray grains under uniaxial loading conditions.