A three-dimensional numerical finite element modeling method is applied to compare interfacial residual thermal stress distribution in AlN single crystals grown by using different substrates such as silicon carbide, boron nitride, tungsten, tantalum carbide, and niobium carbide. A dimensionless coordinate system is used which reduces the numbers of computations and hence simplifies the stress analysis. All components of the stress distribution, both in the film and in the substrate, including the normal stress along the growth direction as well as in-plane normal stresses and shear stresses are fully investigated. This information about the stress distribution provides insight into understanding and controlling the AlN single crystal growth by the sublimation technique. The normal stress in the film at the interface along the growth direction and the shear stresses are zero except at the edges, whereas in-plane stresses are nonzero. The in-plane stresses are compressive when TaC and NbC substrates are used. A small compressive stress might be beneficial in prohibiting crack growth in the film. The compressive stress in the AlN is lower for the TaC substrate than that for the NbC. Tensile in-plane stresses are formed in the AlN for 6H-SiC, BN, and W substrates. This tensile stress in the film is detrimental as it will assist in the crack growth. The stress concentration at the edges of the AlN film at the interface is compressive in nature when TaC and NbC are used as a substrate. This causes the film to bend downward (i.e., convex shape) and assist it to adhere to the substrate. The AlN film curves upward or in a concave shape when SiC, BN, and W substrates are used since the stress concentration at the edges of the AlN film is tensile at the interface and this may cause detachment of the film from the substrate.