Insights into wave propagation in prestressed media are important in geophysical applications such as monitoring changes in geo-pressure and tectonic stress. This can be addressed by acoustoelasticity theory, which accounts for nonlinear strain responses due to stresses of finite magnitude. In this study, a rotated staggered grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer absorbing boundary is used to solve the relevant acoustoelastic equations with

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... hird-order elastic constants for elastic wave propagation in prestressed media. We partially verify our numerical simulations by the plane-wave theoretical solution. Comparisons of theoretical and calculated wave velocities are conducted for both P-wave and S-wave as a function of hydrostatic prestresses. We discuss several aspects of the numerical implementation. Numerical acoustoelasticity simulations for wave propagation in single- and double-layer models are carried out under four states of prestresses, confining, uniaxial, pure-shear, and simple-shear. The results display the effective anisotropy of elastic wave propagation in acoustoelastic media, illustrating that the prestress-induced velocity anisotropy is of orthotropic features strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestressed conditions on seismic responses in both phase and amplitude.