The reflection and transmission coefficients of elastic waves are calculated numerically at the interface (solid–solid) for general anisotropic media oriented in any arbitrary direction. The plane‐wave solutions in anisotropic media are considered. The eigenvalues (slownesses) and the eigenvectors (polarizations) are computed from the 6×6 system matrixAof each medium using a numerical approach. Thezcomponent of the Pointing vector and the radiation condition are used to separate the up‐ and down‐going propagations. The solution of reflection and transmission coefficients at the interface are computed in terms of a scatterer operator approach (connecting the up‐ and down‐going wave components of the two sides of the interface). In this procedure, all the possible wave types (nine combinations as: @/iqP−qP, qP−S1, qP−S2, S1−qP, S1−S1, S1−S2, S2−qP, S2−S1,@/r andS2−S2) of the reflection and the transmission coefficients are at the interface. It is preferable to represent the coefficients as a function of slowness, rather than the conventional angle of incidence, because a common reference forPandSwaves can be used, thus displaying many of the characteristics more clearly. The coefficients depend, in general, on the polar and azimuthal angles of incidence, and the relative values of the elastic constants in the media on the two sides of the interface. Results for fractured media are presented. Some comparisons with the isotropic model are also presented to clarify the behavior of wave propagation in anisotropic media. Complete synthetic waveforms from an explosion source are computed to observe the effects of anisotropy on amplitude and phase at both sides of the interface.