A numerical study of dislocation density is carried out by 3D and time-dependent analysis using the Alexander-Haasen model to estimate growth direction dependence of plastic deformation of Al 2 O 3 single crystals during the annealing process. The direction of crystal growth is set to c-, a-, and m-axes. The calculated results show distribution of dislocation density in the crystal grown in the c-axis has a sixfold symmetry while those in the crystals grown in the aand m-axes show asymmetric distribution. Dislocation densities in the aand m-axes Al 2 O 3 crystals are larger than that in the c-axis crystal.