The results of numerical simulations of acoustic wave propagation and dispersion in the nonmagnetic solar subphotosphere are presented. Initial equilibrium density and pressure stratifications are taken from a standard solar model but modified to suppress convective instabilities in fully compressible two-dimensional ideal hydrodynamical modeling. Acoustic waves are generated by sources located below the height corresponding to the visible solar surface. The dynamic response of the solar interior to two acoustic source types, namely a harmonic source and one representing downward-propagating photospheric plumes, is studied. A large number of randomly distributed localized cooling sources with random amplitudes is also introduced. The methods used to analyze the simulation data are similar to ones used in observational studies in local helioseismology. Time-distance diagrams of the pressure and vertical velocity perturbations at the level corresponding to the solar surface show the appearance of wave packets propagating with different speeds, which are reflected at different depths beneath the subphotosphere. The (ω, kh) power spectra, derived from the vertical velocity data, show the existence of g-, f-, and p-modes; p-mode ridges are identifiable up to high radial orders of n ≈ 11; g-modes appear in the simulations, unlike in the real Sun, where they cannot propagate in the convectively unstable solar subphotosphere. Cross-correlation analysis of vertical velocity perturbations shows a good correspondence with the observed time-distance helioseismic data for quiet Sun. Thus, the ability of the implemented approach of forward modeling to investigate propagation of acoustic, internal, and surface gravity waves in a realistic solar interior model is shown.