A model is developed to investigate the formation and maintenance of wolf territories based on the spatial patterns observed in northeastern Minnesota. Initially we simplify the model to consider the movements of a single pack. In this case we obtain steady state density distributions corresponding to territories and determine how the size of a territory depends on the number of wolves in a pack. We suggest how, with sufficient access to the relevant field data, this simplified model could be used to estimate some of the model parameters. The complete multi-pack model shows how interactions between adjacent packs determine the shape of the territory. We investigate the solutions to the mathematical model systems and discuss ecological implications.