Summary Migration of the Kirchhoff type is based on a diffraction stack. It is a task of high computational effort. A major contribution to the costs is the determination of the stacking surface, i.e. generation of large amounts of traveltime data. Whereas the demands in CPU time and computer storage are high already for isotropic media, they become even higher as soon as anisotropy is con- sidered, since the traveltime computation in anisotropic media requires a magnitude more in computational time than in isotropic media. In this paper we propose a tech- nique of traveltime interpolation for arbitrary anisotropic media that is accurate and effcient in terms of CPU time as well as in storage.