Growth of GaN on Si substrate is a popular topic due to its good thermal conductivity,low cost,easy to obtain large size.However,it is still difficult to achieve GaN on Si substrate with high quality because of the large lattice mismatch and thermal mismatch.In this paper,thermal stress analysis of GaN epilayers grown on Si substrate with AlxGa1-xN interlayers has been investigated theoretically.A finite element model based on coupled field was established to analyze and design high quality GaN epilayers grown on Si substrate with thin variable composition graded AlxGa1-xN interlayers.