Based on the finite element approach,we investigated the strain field distribution of GaN/AlN self-organized quantum dot.The truncated pyramid shaped quantum dot that has been found in experiment was adopted as the physical model,and the material elastic constants used in this paper is wurtzite structure.In dealing with the lattice mismatch,we employed a three-dimension anisotropic pseudo thermal expansion of the island.We compared the calculated results with that calculated by Green's function theory in which lots of assumption is adopted,and the results prove the corrections of our model.In the final,the anisotropic of the material is discussed,and the conclusion is that the anisotropin has no influence on the vertical alignment of inter-layered quantum dots.Our model didn't adopt the assumptions used in the Green's function approach,so better reliability and precision results are obtained.