A three-dimensional (3D) Ansys model which is comprised of the GaN films and Al2O3 substrate is developed to simulate the thermal stress and displacement from the difference of thermal expansion coefficient between two kinds of materials. The 3D model is used to analyze the thermal stress and displacement in GaN films under different deposition temperatures, GaN films thickness, Al2O3 substrate thickness and diameters by the simulating orthogonal test. The influence of the above mentioned factors on the thermal stress and displacement in GaN films is analyzed, and the optimum level combination of factors to minimize the thermal stress and displacement in GaN films is determined. The error between the theoretical and numerical solution of GaN films stress is less than 1.4%. The developed model can be used to analyze the minimum thermal stress and displacement in GaN films. From big to small, the order of the effect of all kinds of factors on the thermal stress in GaN films is the deposition temperature, films thickness, substrate thickness and diameter. The most optimum combination is A1B3C3D1 to minimize the thermal stress. For the displacement in GaN films, the order is the substrate diameter, films thickness, substrate thickness and deposition temperature, and the most optimum combination is A1B3C3D1 for the deposition temperature.