There is considerable interest in the study of self_assembled quantum dots as on e of the new optoelectronic materials in the field of physics. It is interest ing in theory, and also applications. In this article, we consider the InAs isla nds buried in GaAs, because of large lattice mismatch (≈-0.067), which makes s t rain effect to be the main factor in the formation of quantum dots. Most methods for calculations of strain distribution are based on the numerical solution of qu antum dots structures, which need heavy calculations work. We present a detailed process to derive an analytical formula for the strain distribution in some f am iliar shapes of quantum dots with Green function method, and discuss their influ ence on the strain distribution in quantum dots by taking into account the anisotr opy of elastic properties and shape. The results showed that the strain distribu t ions in the major part of the quantum dot structure are very similar for differe nt shapes and that the characteristic value of the hydrostatic strain component depends o nly weakly on variation of the shape of quantum dots.