An ideal way of fabricating quantum dots is by self-assembly that can be simulated using the Stranski-Krastanow growth mode. This paper presents a numerical scheme to Simulate the morphology of the quantum dot "island" due to stresses induced by a buried quantum dot. The surface diffusion equation that governs epitaxial growth is solved for the normal surface velocity by using a meshfree interpolation technique-the moving least square method. The normal surface displacement is then deduced and the process is repeated through a difference scheme to obtain the change in surface shape as a function of time. Simulations using the present method have found that the island morphology is affected by various factors including elastic anisotropy, cap layer thickness and crystal orientation. (c) 2004 Elsevier B.V. All rights reserved.