Prolonged disruption to aviation during the April–May 2010 eruption of Eyjafjallajökull, Iceland resulted in pressure to predict volcanic ash plume concentrations for the purpose of allowing aircraft to fly in regions with low ash contamination. Over the past few decades there have been a number of incidents where aircraft have encountered volcanic ash resulting in damage to the aircraft and loss of power to engines. Understanding the volcanic ash concentrations that these aircraft have encountered provides important input to determining a safe concentration limit.Aircraft encounters with six volcanic eruption plumes have been studied and ash concentrations predicted using the atmospheric dispersion model NAME. The eruptions considered are Galunggung 1982, Soputan 1985, Redoubt 1989, Pinatubo 1991, Hekla 2000 and Manam 2006. Uncertainties in the eruption source details (start time, stop time and eruption height) and in the aircraft encounter location and flight path are found to be major limitations in some cases. Errors in the driving meteorological data (which is often coarse in resolution for historic studies) and the lack of eruption plume dynamics (e.g. umbrella cloud representation) results in further uncertainties in the predicted ash concentrations.In most of the case studies, the dispersion modelling shows the presence of ash at the aircraft encounter location. Maximum ash concentrations in the vicinity of the aircraft are predicted to be at least 4000 μg m−3 although confidence in the estimated concentrations is low and uncertainties of orders of magnitude are shown to be possible.