The aim of this paper is to demonstrate the potential of using the system dynamics computer simulation methodology to gain insight into the dynamic behavior of insurgencies. To this end, a basic model of insurgencies containing the dynamic mechanisms of incident suppression, insurgent creation, and war weariness is developed. The paper then shows how this model, properly adapted, can explain much of the behavior of insurgencies by examining the Anglo-Irish War of 1916-21. Then, to illustrate the potential usefulness of the system dynamics methodology to policy makers, the paper uses the model to determine which system parameters might have most affected the outcome of the Anglo-Irish War. As one example, the simulation suggests that the lack of British governmental legitimacy in Ireland may have hindered the simulated efficacy of insurgency suppression efforts. As another example, the paper shows how the effects of a “good works” policy might have aided insurgency suppression in Ireland by separating the insurgents from their supporting population. The paper then concludes by proposing how such a model and the system dynamics methodology in general might be developed to assist policy makers manage current insurgencies throughout the world.