Determination of mechanism of anisotropic growth, dot formation, crystal orientation determination and polarity determination for epitaxial growth are introduced as examples of application of the density functional calculation and the kinetic Monte Carlo simulation. The anisotropic atomic migration for non-polar surface of GaN and ZnO forms stripe-structure during epitaxial growth. The adsorption site and adsorption energy of adatom determine polarity and orientation of compound semiconductor in epitaxial growth.