A novel solution approach is proposed for the numerical simulation of the solidification process of binary Al-Si hypoeutectic alloys during upward and downward solidification modes. Undercooling is always observed during solidification, but the phenomenon could not be considered in the present-day numerical solution. In this approach, the temperature distribution in the mushy zone was used to define the fraction of solid, which enabled the evaluation of the effect of dendrite tip undercooling on the characteristics of the binary alloy solidification. The present numerical algorithm was found to significantly reduce the computation time. Transient temperature distribution and solidification time from the numerical analysis, with consideration of natural convection due to temperature and concentration gradients, have been successfully simulated and validated with experiment results. Numerical results with consideration of dendrite tip undercooling have better agreement with experimental results. The effect of dendrite tip undercooling on the fluid flow (velocity profile), G, R and λ1 for both upward and downward solidification modes of Al-Si alloys have been investigated and discussed. Consideration of undercooling was found to increase G and reduce R in both solidification modes. During downward solidification, considering undercooling significantly increased flow velocity and decreased λ1. The primary dendrite arm spacing could be validated with results from uni-directional solidification experiments only when dendrite tip undercooling was considered.