In this study, the elastic properties of two high-pressure polymorphs SiO2 nanostructure, stishovite and CaCl2-type, are obtained using Density Functional Theory in 0-80 GPa high pressure domain at zero temperature, based on reducing an interacting many-electron problem to a single-electron problem. It is shown that below 40 GPa, the stishovite phase is more stable; superior to this limit, the CaCl2-type phase becomes more stable, using Gibbs free energy method. Furthermore, the pressure dependence of the density, volume, bulk, and shear moduli were defined in the selected pressure domain.