Abstract. Devastating tsunami over the last decade have significantly heightened awareness of the potential consequences and vulnerability to tsunami for low-lying Pacific islands and coastal regions. Our tsunami risk assessment for the atolls of the Tokelau Islands was based on a tsunami source–propagation–inundation model using Gerris Flow Solver, adapted from the companion study by Lamarche et al. (2015) for the islands of Wallis and Futuna. We assess whether there is potential for tsunami flooding on any of the village islets from a series of fourteen earthquake-source experiments that apply a combination of well-established fault parameters to represent plausible "high-risk scenarios" for each of the tsunamigenic sources. Earthquake source location and moment magnitude were related to tsunami wave heights and tsunami flood depths simulated for each of the three atolls of Tokelau. This approach was adopted to yield indicative and instructive results for a community advisory, rather than being fully deterministic. Results from our modelling show that wave fields are channelled by the bathymetry of the Pacific basin in such a way that the swathes of the highest waves sweep immediately northeast of the Tokelau Islands. From our series of limited simulations a great earthquake from the Kuril Trench poses the most significant inundation threat to Tokelau, with maximum modelled-wave heights in excess of 1 m, which may last a few hours and include several wave trains. Other sources can impact specific sectors of the atolls, particularly from regional sources to the south, and northern and eastern distant sources that generate trans-Pacific tsunami. In many cases impacts are dependent on the wave orientation and direct exposure to the oncoming tsunami. This study shows that dry areas remain around the villages in nearly all our "worst-case" tsunami simulations of the Tokelau Islands. Consistent with the oral history of little or no perceived tsunami threat, simulations from the recent Tohoku and Chile earthquake sources suggest only limited flooding. Where potential tsunami flooding was inferred from the modelling, recommended minimum evacuation heights above local sea level were compiled, with particular attention paid to variations in tsunami flood depth, subdivided into directional quadrants around each atoll. But complex wave behaviours around the atolls, islets, tidal channels and lagoons were also observed in our simulations. Wave amplitudes within the lagoons may exceed 50 cm, increasing any inundation and risks on the inner shoreline of the atolls, which may influence evacuation strategies. Our study shows that indicative, but instructive, simulation studies can be achieved even with only basic field information, due in part to the relative simplicity of the atoll topography and bathymetry.