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A numerical formulation based on the weighting function scheme is developed in the present investigation for convection-conduction phase change problems. The solid phase is regarded as a liquid having an infinite viscosity. Such a treatment allows the stream-vorticity formulation to apply over the entire physical domain including the liquid-solid interface. The weighting function scheme then is used to handle the sharp viscosity jump at the liquid-solid interface. A problem dealing with pure tin is employed to test the performance of the present method. The predicted interface profiles are found to agree with available experimental data qualitatively. The computation effort required by the present numerical technique, however, is less than 2% ofthat needed by a two-region method for this same problem. Unlike the existing single-region methods, the present numerical technique produces smooth streamlines and isotherms even in the vicinity of the solidification front.