The formulation of suitable boundary conditions at the water-ice interface during ice formation (melting) is an important aspect of the sea-ice coupled model. The transfer of water and salt through the water-ice can be posed as different boundary conditions. Behavior of the model under these boundary conditions is illustrated through simple analytical models and a numerical model based on pressure-? coordinate. It is emphasized that the correct handling of the boundary conditions associated with sea ice formation requires an accurate treatment of the equivalent pressure on the top of water column and the total volume (mass) of the water column in the ice formation regime. Improper treatment of these boundary conditions may lead to an artificial loop current near the edge of ice in numerical simulations of oceanic circulation in the Arctic Ocean or near the Antarctica.