In this study, normal grain growth and stressed grain growth are simulated in a copper polycrystalline thin film as a representative volume element (RVE) considering isotropic and anisotropic grain boundary energy properties using phase field theory. Our phase field theory is a thermodynamically consistent method for solving interfacial problems like microstructure evolution. Two main parameters are dominant in grain boundary migration: grain boundary energy and grain boundary mobility. These parameters are included in phase field equations using physical parameters defined in phase field model. If grain boundary energy and mobility remain constant for all grain boundaries, the grain boundary is called isotropic. On the other hand, if the grain boundary energy and mobility have different values for each grain boundary, the grain boundary is called anisotropic. We studied normal and stressed grain growth under shear and elongation conditions. The stress effect due to the elastic deformation is included as elastic strain energy term to the grain boundary energy term. The loading is applied as a constant uniaxial strain by applying the deformation to an element in ABAQUS and the phase field equations are solved by using a UMAT subroutine. The texture and therefore the total elastic stiffness of the RVE will be changed under loading. Changing of elastic tensor causes the stress to be changed under constant strain called stress relaxation. Computer simulations are performed for isotropic and anisotropic cases and the results are compared. The anisotropic grain boundary energy is calculated by Read-Shockley equation which is based on the dislocation theory for low angle tilt boundaries. In this equation, the grain boundary energy depends on two parameters: the in plane misorientation between the neighbouring crystals which is the difference between the crystal orientations and the inclination of grain boundary which is the angle between the bisector of misorientation and the normal to the grain boundary. According to this equation, the grain boundary energy is the same as the isotropic case for high angle tilt boundaries. But for low angle boundaries (less than 15?), the grain boundary energy is less than the isotropic case. So the anisotropic energy is generally less or equal to the isotropic case. The simulations show that the misorientation dependent anisotropy has a significant influence on texture evolution and the changing of polycrystalline macroscopic properties. For example, decreasing the rate of grain growth, aggregation of the grains with similar orientations, stretched grains and decelerating the rate of stress decreasing in stress relaxation are some phenomena which have been observed. These observations are due to the Read-Shockley misorientation dependent term which makes the low angle boundaries to be more resisting in the RVE. The inclination dependency means that different inclinations have different energies. For example, in a circular bicrystalline, the circular boundary will remain circular in shrink or growth. But in inclination dependent anisotropy, the circular boundary will attain a square shape in shrink and a rhombus shape in growth. The results show that inclination dependent anisotropy has no significant effect on grain growth rate and just controls the grain boundary shape. This point causes the inclination anisotropy to have no effect on polycrystalline texture and therefore no effect on mechanical properties. Keywords: Anisotropic grain boundary, Polycrystalline microstructure, Phase field theory, Computer simulations