A simple deterministic model is described which models the behaviour of the krill fishery in Subarea 48.1 and estimates the effort applied and the catch of krill in fine-scale squares. Parameters for the model are calculated from data reported to CCAMLR by Chile over the period 1989 to 1992. The distribution of catches predicted by the model, which is restricted to the months December to March, compare favourably with the general distribution of catches in Subarea 48.1. A number of management scenarios are considered, which involve closures (i) of a zone 50 km offshore from the South Shetland Islands, and (ii) of zones 100 km around Livingston and Elephant Islands. The model predicts that the management option of closing the zones around Livingston and Elephant Islands in alternate years would result in an average yearly catch similar to that at present, although the catch is much more concentrated in foraging areas of land-based predators in alternate years under this scenario.