Impedance-like boundary conditions are successfully applied in different fields of physics and material science. However, they are not very well-known in seismology. The purpose of this paper is to discuss potential applications of these boundary conditions in the framework of theory of elastic wave propagation with emphasis on seismology. Generally, such boundary conditions are always interesting in those cases, where the influence of any body on a wave field in its interior is to be described by an integral effect on its surface (keyword: equivalent boundary conditions). It is well-known that we meet a great variety of different boundaries in the Earth's interior. Basically, the contact between two solids is a complicated phenomenon. However, for the interaction of seismic waves with discontinuities very often an ideally welded contact is assumed which implicates continuity of the relevant displacement and stress components. This is only a first approximation which can be and must be extended. It is not unusual to assume contact planes as very thin layers which results in the formulation of novel boundary conditions.
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