The transient freezing of liquid metals in laminar flow in the thermal entry region of a circular tube is investigated analytically under the assumption that the heat removal from the tube wall is by convection into an environment at a temperature lower than the freezing temperature. The variation of the solid-liquid interface as a function of time and position along the tube is determined. The effects of Biot number and the difference between the freezing and the ambient temperatures on the length of freeze-free zone are examined.