Residual thermal stress distribution in AlN single crystal, grown on tungsten as a crucible material, was investigated using a numerical study. It has been demonstrated that a three-dimensional, instead of a two-dimensional, formulation predicts significantly greater values of stress. Dimensionless coordinates were used to essentially simplify the stress analysis and reduce the number of calculations. In addition, thermoelasticity approach simplifies the study of stresses for a nonstationary temperature field. The stress in the AlN film along the thickness or  growth direction is essentially zero but the in-plane stress is large. The stress at the corner of the film is much higher due to stress concentration and could cause formation of microcracks. The stress in the film is tensile while that in the substrate is compressive, which causes a reversal of the stress across the interface. Separation or delamination of the film from the substrate could occur due to this reversal of the stress at the interface. The stress decreases as the thickness of the film increases or the thickness of the substrate decreases. Thus, formation of microscopic cracks in the film could be avoided by using a thinner substrate. The analysis on interaction of neighboring islands in order to simulate coalescence of island growth indicates stress concentration at the boundaries of the islands, which could produce threading dislocations and hence polycrystalline growth. The analysis of the effect of misorientation of the neighboring grains on the residual thermal stress in the film has shown that a large stress can develop at the grain boundary and can lead to grain boundary cracking.