Using extended kinetiń model, we have shown that layer-by-layer epitaxial growth realized in definite interval of temperatures at definite external molecular flux. Different physical processes during the film growth have been considered. Influence of these processes on the optimal values of technological parameters and stability of growth front were investigated. Computer simulations have shown that appearance of layer-by-layer growth depends on two dimensionless parameters. Numeric results allowed us to analyze surface transformation during growth. It is known that Enrich-Swebel effect (ES) has negative influences on morphology of thin film. Interlayer transport is slowed by ES-barrier, with even optimal external parameters. The ES effect is considered in the model of the epitaxial growth. To verify this model with experimental data, we examine it for system Cu/Cu(100). This model is appeared to agree with experiment for given system.