Monte Carlo simulation of smoothing and step-terraced morphology formation on the Kossel crystal surface is carried out. The simulation results are compared with the experimental data on GaAs surface smoothing in equilibrium conditions. Despite the simplicity of the Kossel crystal model, the simulation qualitatively describes the experiment. The full length of monatomic steps and the mean size of islands on terraces are explored for quantitative characterization of the surface relief evolution. The comparison of the simulation and experiment yields surface diffusion activation energy E-d = 1.3 +/- 0.05 eV, lateral bond energy E-b = 0.32 +/- 0.02 eV and adatom desorption energy E-des = 2.1 +/- 0.05 eV, which are in reasonable agreement with the values obtained earlier from GaAs growth experiments and ab initio calculations. (C) 2015 Elsevier B.V. All rights reserved.