A computer simulation of North American end-Pleistocene human and large herbivore population dynamics correctly predicts the extinction or survival of 32 out of 41 prey species. Slow human population growth rates, random hunting, and low maximum hunting effort are assumed; additional parameters are based on published values. Predictions are close to observed values for overall extinction rates, human population densities, game consumption rates, and the temporal overlap of humans and extinct species. Results are robust to variation in unconstrained parameters. This fully mechanistic model accounts for megafaunal extinction without invoking climate change and secondary ecological effects.