A model of the fluid flow in a thin walled continuous caster is proposed. The stability of the flow is considered when the viscosity is temperature dependent. Mathematically the model can be described as a Hele-Shaw cell with heat loss. A condition for the growth of an uneven flow distribution in the cell is derived. This condition is related to the change in viscosity with the temperature of the liquid metal being cast, and the rate at which it is being cooled. An unstable flow distribution in the mould makes the continuous casting process difficult to control and can cause 'lock-ups' and 'breakouts'.