Averaging the anisotropy of each crystal, the macroscopic behavior of polycrystalline materials is isotropic and homogenous in terms of elastic deformation. However, the anisotropic property of each crystal influences on the local stress field ahead of a crack tip if the crack size is not large enough in comparison with the grain diameter. This brings about the change in the crack driving force (CDF) such as stress intensity factors. In the present study, in order to investigate the cause and magnitude of the change in the CDF, the finite element analysis is performed. The calculations are carried out for a single crystal model, a bi-crystal model, and a polycrystal model containing a transgranular or an intergranular semi-circular crack. The results implied that the magnitude of CDF is dependent not only on the crystal orientation but also on the deformation-constraint caused by the difference in elastic modulus of grains near the crack tip. The statistical scatter of CDF due to the random crystal orientation in a polycrystal is examined by a Monte Carlo simulation. The variation in the SIF becomes small as the crack size increases.