The Earth's subsurface is an anisotropic medium where the velocity of seismic waves alters in different propagation angles. Omitting anisotropy in seismic imaging not only brings mis-positioning of migrated dipping events but also fails to retain dipping energy during dip-moveout. To account for the efficacy of seismic anisotropy in imaging, an anisotropic wave equation must be engaged. Seismic traveltime computing is fundamental of both Kirchhoff migration and tomography algorithms. Two main categories of traveltime computing involve traditional ray tracing methods and finite difference eikonal solvers. In this study, we present two techniques of initial-value ray tracing and fast marching eikonal solver in isotropic and vertical transverse isotropy (VTI) media, and a comparison between results is demonstrated for more evaluation. Although the ray tracing approach is able to compute multiple arrivals with great precision, the eikonal solver is faster and more robust for traveltime computation. Since the ray tracing result is not a deterministic solution and it depends on the initial circumstance, employing the eikonal solver method are more preferred and suggested. © Published under licence by IOP Publishing Ltd.