A stochastic model for the MBE growth of Ge is developed based on the master equation approach with solid-on-solid restriction and quasi-chemical approximation. The surface kinetic processes included are: adsorption, evaporation and intralayer and interlayer migrations. The growth rate, the average surface roughness and the average intensity of reflection high energy electron diffraction (RHEED) (using kinematical theory of electron diffraction’ were obtained for the MBE growth of Ge with the temperature in the range 100-500°C and a typical flux of 1 Å/sec. The average surface roughness and the growth rate are found to be independent of substrate temperature below 150°C and above 400°C. In the intermediate temperature range, the growth rate increases and the surface roughness decreases with increasing temperature. The kinetic roughening temperature above which a smooth surface remains smooth, is identified from the temperature depen-dance of the average surface roughness and RHEED intensity, as 400°C. The temperature dependance of the average RHEED intensity and the kinetic roughening temperature obtained from this study compare favorably with the experimental results. At low substrate temperature, the surface migration rate is negligible irrespective of the temperature and therefore, the surface roughness and the growth rate become independent of the growth temperature. At high substrate temperatures, the surface roughness and the growth rate attain the limiting values for the flux chosen, owing to the saturation of the available sites for the interlayer migration process. Thus, these parameters become independent of the growth temperature.