Silica aerogels are highly porous 3D nanostructures and have exhibited excellent physio-chemical properties. Although silica aerogels have broad potential in many fields, the poor mechanical properties greatly limit further applications. In this study, we have applied the finite volume method (FVM) method to calculate the mechanical properties of silica aerogels with different geometric properties such as particle size, pore size, ligament diameter, etc. The FVM simulation results show that a power law correlation existing between relative density and mechanical properties (elastic modulus and yield stress) of silica aerogels, which are consistent with experimental and literature studies. In addition, depending on the relative densities, different strategies are proposed in order to synthesize silica aerogels with better mechanical performance by adjusting the distribution of pore size and ligament diameter of aerogels. Finally, the results suggest that it is possible to synthesize silica aerogels with ultra-low density as well as high strength and stiffness as long as the textural features are well controlled. It is believed that the FVM simulation methodology could be a valuable tool to study mechanical performance of silica aerogel based materials in the future.