The characteristics of sound transmission into real, or dissipative, media differ from those of transmission into lossless media. In particular, when a plane wave in a fluid is incident upon a real, dissipative elastic material, the transmitted waves are in general inhomogeneous, even when the incident wave is itself homogeneous and incident at a sub-critical angle; and more significantly, energy transmission occurs even above the critical angle. In addition, for any real incidence angle, the parameters of an incident inhomogeneous wave may be tuned so that there is no reflection from the surface of a viscoelastic solid. That phenomenon may be exploited in applications requiring energy transmission into solids. In this work, the transmission of incident inhomogeneous, as well as homogeneous, acoustic waves into solid materials is characterized; a hysteretic damping model is assumed. Numerical results are presented for the transmitted stress and energy distributions for typical solid materials, including polymer-based solids. The conditions for total transmission, i.e., no reflection at the interface, are explored, where the propagation angle, degree of inhomogeneity, and frequency of the incident wave are varied for a given material. These investigations show substantial transmission gains in the vicinity of the zero of the reflection coefficient, compared to homogeneous incident waves
