In the past decade IceCube's observations have revealed a flux of astrophysical neutrinos extending to 107GeV. The forthcoming generation of neutrino observatories promises to grant further insight into the high-energy neutrino sky, with sensitivity reaching energies up to 1012GeV. At such high energies, a new set of effects becomes relevant, which was not accounted for in the last generation of neutrino propagation software. Thus, it is important to develop new simulations which efficiently and accurately model lepton behavior at this scale. We present TauRunner, a Python-based package that propagates neutral and charged leptons. TauRunner supports propagation between 10GeV and 1012GeV. The package accounts for all relevant secondary neutrinos produced in charged-current tau neutrino interactions. Additionally, tau energy losses of taus produced in neutrino interactions are taken into account, and treated stochastically. Finally, TauRunner is broadly adaptable to divers experimental setups, allowing for user-specified trajectories and propagation media, neutrino cross sections, and initial spectra. Program title:TauRunner CPC Library link to program files:https://doi.org/10.17632/82nyd9skhj.1 Developer's repository link:https://github.com/icecube/TauRunner Licensing provisions: GNU General Public License 3 Programming language:Python Nature of problem: Propagation of ultra-high energy neutrinos in dense media accounting for various effects associated with ντ and τ± energy losses. Solution method: Monte Carlo methods.