A numerical model of brine-induced circulation is used to study circulation in the lagoons and shelf waters of the Beaufort Sea. The model solves the equations of motion, continuity, and salt transport. The salt flux is set as a functin of the salinity difference between growing sea ice and seawater and the rate of ice growth. Several experimental runs show that under-ice haline circulation is controlled by salt flux and bottom configuration. An idealized model of a shallow Arctic lagoon gives currents of 1 cm s-1 for brine-induced circulation under landfast ice. This agrees very well with observations.