Approximate PP plane wave displacement coefficients of reflection and transmission for weak contrast interfaces separating weakly but arbitrarily anisotropic elastic media are presented. The PP reflection coefficient for such an interface has been derived recently by Vavrycuk and Psencik (1997). The PP transmission coefficient presented in this paper was derived by the same approach. The coefficients are given as a sum of the coefficient for the weak contrast interface separating two nearby isotropic media and a term depending linearly on contrasts of the so-called weak anisotropy (WA) parameters (parameters specifying deviation of properties of the medium from isotropy), across the interface. While the reflection coefficient depends only on 8 of the complete set of the WA parameters describing P wave phase velocity in weakly anisotropic media, the transmission coefficient depends on their complete set. Tests of accuracy of the approximate formulae are presented on several models.