The Norse who settled and lived in Greenland AD 1000–1500 provide a unique biological anthropological material for the investigation of human and environmental interaction. They were a relatively isolated population, constrained in both space and time. This study reports on demographic modelling of (1) marriage and fertility patterns and (2) total population level numbers with crude death rates and birth rates, including immigration and emigration scenarios. In addition to linear models, I also used stochastic models, which may be especially important when dealing with small populations. My results indicate that a small population such as the Norse inevitably will be close to a minimum sustainable level, and that simple emigration may explain the demise of the settlements. Furthermore, when the societal and economical implications of the population dynamics are considered, certain activities of the Norse in the latter phase of the settlement, such as the building of new churches, may acquire a new significance. To illustrate this, a so-called sunk-cost economic model was applied.