A model for face centered cubic binary interstitial alloys and advance the theory of elastic deformation and wave propagation within these alloys using the statistical moment method are presented. The theory extends to include the elastic properties and wave dynamics of pure metals as a subset. The numerical simulations for metals like Au and Cu, as well as the CuSi alloy are conducted. The results obtained for Au and Cu were validated against experimental data and existing calculations. For the CuSi alloy, numerical predictions offer insights that could be confirmed by future experiments.