Using isotropic inversion of teleseismic P-travel times computed for laterally varying anisotropic structures, we investigate how anisotropy may show up in classical tomographic studies based on isotropic 3-D inversions. Anisotropic bodies of several tens of kilometers in the upper mantle may significantly bias the estimation of the isotropic part of a P-wave velocity image. The largest artifacts are introduced by anisotropic bodies with a dipping olivine a axis which could be associated with fossil subduction zones. However, anisotropy-induced artifacts are negligible for anisotropy caused by pure shear deformation of the lithosphere due to horizontal extension or compression. The negative P-wave velocity anomaly arising from isotropic inversion beneath a rift zone may be enhanced if the olivine crystal's a axes are preferentially oriented parallel to the asthenospheric flow along the rift axis. Examination of recently published tomographic models shows that the image of the Rhine Graben may contain significant anisotropic artifacts. ¿ 1999 American Geophysical Union