We develop a thermal-elastic stress model using the finite element method to predict three-dimensional anisotropic stress in AlN single crystals homoepitaxially grown by the physical vapor transport process; we also perform numerical experiments for a 1-in. AlN crystal surrounded by different cone-tube designs and grown along various orientations. The influences of the cone-tube shape and the growth orientation on the stresses inside the AlN crystal are investigated in detail. The simulation results show that the von Mises stress exceeds 1.11 GPa under all specified growth conditions, while the anisotropy is negligible. The resolved shear stresses are strongly dependent on the thermal gradient inside the growing crystal and the growth orientation. Strong anisotropy of the resolved shear stress is observed upon tilting of the growth orientation. The resolved shear stress along {0001}⟨112̅0⟩ primary slip system reveals that the c-axis growing crystal is under tensile stress along all three primary slip directions. Nevertheless, an inversion of the resolved shear stress from tensile to compressive along the −a 3 slip direction is observed when changing the growth orientation. The total resolved shear stress shows 6-fold symmetry, reflection symmetry and 2-fold symmetry along [001], [10√3], and [100] growth orientations, respectively.