Generally there is no separation of shear and compressional wave in inhomogeneous media.They are generally coupled at every point of inhomogeneity, interface, or boundary.

In layered media, however, consisting of a stack of homogeneous layers, bounded by impenetrable boundary or homogeneous infinite half spaces, it is usual to separate vertically polarized compressional-shear wave systems (P-SV waves) from horizontally purely shear wave systems (SH waves) as in seismology. The separation of the vertical (V) and horizontally (H) polarized wave systems is exact. The two wave systems, P-SV and SH, are only coupled at scattering inclusions embedded in the layered media.

But if your short-wavelength shear waves are only important insofar as they are a loss mechanism for wave systems dominated by compressional waves, then you might be able to ignore the shear waves as such, and include their effect approximately, simply as a loss mechanism for the compressional waves, increasing the absorption of the compressional waves to  account for their energy loss into weak conversion to shear waves at points of inhomogeneity and reflective boundaries. In other words, you model the medium carrying the waves as a lossy fluid bearing compressional waves only. You might do this for sound propagation through silty soft water-saturated mud for instance, as often done in ocean-seismoacoustics.  Seafloor layers often have compressional wave speeds higher than shear, and the relatively short wavelength of the shear waves means that their energy is quickly lost before they propagate very far, and their main effect is as energy loss mechanism for compressional waves.

Note that if you model a solid medium as a fluid this way, then you also have to change boundary conditions to suit. You must use the boundary conditions of a fluid (slip contact), and not the boundary conditions of a solid (welded contact). If  you are using finite elements, then you must use fluid elements and not solid elements. 

Ronald

Thanks for the insight! I am actually most interested in the shear wave propagation in soft tissue. So that pretty much limits to solid medium with nearly incompressible media. Looks like there is no easy ways to cut corners. Bo