This paper presents a finite element method of calculating strain distributions in and around the serf-organized GaN/A1N hexagonal quantum dots.The model is based on the continuum elastic theory,which is capable of treating a quantum dot with an arbitrary shape.A truncated hexagonal pyramid shaped quantum dot is adopted in this paper.The electronic energy levels of the GaN/A1N system are calculated by solving a three-dimension effective mass Shr(o)dinger equation including a strain modified confinement potential and polarization effects.The calculations support the previous results published in the literature.