This paper investigates numerically the effect of natural convection on the solidification of laminar fluid flow in the thermal entrance region of a horizontal isothermally cooled tube. The theoretical solution assumes that the Prandtl number is large, and the variation of the liquid-solid interface is gradual in the axial direction. For the liquid phase, a vorticity stream function equation is formulated and solved by a boundary vorticity method. The significance of the natural convection effect is found to depend on the local Rayleigh number. A circular liquid-solid interface is assumed with its center moving up gradually away from the tube axis. The growth of the solid shell is strongly influenced by the superheat ratio lambda., the Rayleigh number and the axial position. The theoretical analysis yields the profiles of liquid-solid interface, pressure drop and heat transfer coefficient with varying axial location for the cases of 0 less than or equal to Ra less than or equal to 10(7) and 0.1 less than or equal to lambda less than or equal to 10. The numerical predictions agree fairly well with the existing experimental data for the heat transfer rate, the pressure drop and the liquid-solid interface.