The investigation of physical and mechanical properties of nitride nanowires (NWs) is a topical field of modern nanotechnological research due to a wide range of promising applications. Normally, the NWs are embedded in a host polymer (e.g., hydrogen silsesquioxane – HSQ), and it becomes necessary to determine the effective properties of polymer-NW compositions rather than of separate wires. The central idea of the present research is the evaluation of the effective elastic moduli of the anisotropic composite HSQ-NW material via the minimization of the goal function that specifies the discrepancy between the measured and calculated characteristics of laser-generated surface acoustic waves. The experimental data are obtained on the basis of transient grating spectroscopy while the theoretical dispersion curves are calculated using the analytically based computer model for elastic guided wave excitation and propagation in multilayered elastic anisotropic half-spaces. The numerical examples illustrate the validation of the developed computer model against the experimental data acquired for sandwich microstructures with known elastic moduli as well as demonstrate the restoration of the latter in the case of HSQ-NW compositions with unknown mechanical properties.