Botswana hosts the world's largest population of African elephants Loxodonta africana, and in northern Botswana, populations are increasing at a rate of 6% per annum, The greatest cash return on a single elephant is from trophy hunting, and hunting is an important foreign income generator. Hunting does, however, risk the sustainability of both the elephant population and the supply of males with trophy-quality tusks. A model utilising a Leslie matrix was developed to simulate the population dynamics of the elephants in northern Botswana under different levels of hunting pressure, with different calf survival rates and with or without a carrying capacity imposed. The age structure of a pristine population, and the proportion of elephants of each age with trophy-quality tusks was developed from tusk measurements and ages of elephants culled over 25 years from Kruger National Park. The model suggests that the current level of hunting pressure is sustainable and unlikely to threaten the availability of trophy-quality tusks in the future. Simulations of increased hunting pressures indicated that doubling the current hunting take-off would result in very few large trophy animals, but would not compromise the supply of males suitable for trophy hunting. A decrease in the current survival rate of calves in their first year of life would, however, greatly reduce the supply of trophy- quality elephants.