Software packages for computing seismic traveltimes and raypaths in an isotropic, spherically symmetric, Earth model are well known and widely used. However, even though the theory for transversely isotropic (TI), spherically symmetric, models has been known since the late 1960s, readily available programs for traveltime calculations are restricted to isotropic models. We have developed a new software package, ANISOtime, for computing seismic traveltimes and raypaths in laterally homogeneous, TI, spherical media. This package calculates traveltime tables for both immediate and subsequent use. ANISOtime has both graphical user interface and command‐line interface modes. The package is available for free public download. As it offers cross‐platform compatibility through Java 8, it runs on Windows, macOS, Unix, and Linux.