The mechanical and thermodynamic properties (such as the nearest neighbor distance, the molar volume, the adiabatic and isothermal compressibilities, the thermal expansion coefficient and the heat capacities at constant volume and at constant pressure) of molecular cryocrystals of many atoms with a face-centered cubic structure such as alpha-CO2, alpha-N2O, at various temperatures and at pressures up to 10 GPa are investigated using the statistical moment method (SMM) in statistical mechanics and compared with the experimental data.