Zirconia film growth on the (001) silicon surface was investigated with the use of several kinetic models available in frame of MD-kMC code: lattice kinetic Monte Carlo (lkMC) model, molecular dynamics model of vapor deposition (MBE model) and integrated kMC-DR model to simulate zirconia film growth in the ALD process. The proposed kMC-DR method combines conventional kinetic Monte Carlo approach with geometry optimization steps (dynamic relaxation). We shown that each above model can be successfully used to study certain aspects of zirconia film growth: film composition in frame of the lkMC model, evolution of the film structure in the MBE model and structure of the ZrO2-Si interface in frame of the kMC-DR approach. The steady state film growth rates obtained from the lkMC and kMC-DR models are in reasonable agreement with experimental results for zirconia film growth rate in an ALD reactor, thus confirming the effect of steric hindrances on the film growth rate. In frame of MBE and kMC-DR models we also found that the zirconium coordination number increases in course of film deposition. The results obtained with kMC-DR approach demonstrate formation of non-uniform ZrO2 film at the first ALD cycles because of the mismatch between the oxidized silicon support and the zirconia bulk structure.