It is well known that fluid flow phenomena in the solidifying zone play a major role in forming macrosegregation and microstructure. In order to understand the interaction of fluid flow in a solidifying medium, unsteady state natural convection both in the liquid pool and in the interdendritic region and solute redistribution due to this natural convection together with changes in the morphology due to fluid flow such as shearing off of the dendrites should be solved simultaneously. Recently, some progress has been made in solving solidification problems considering fluid flow in solidifying ahoy systems. In order to handle fluid flow the interdendritic flow was treated by assuming a Darcy's flow introducing permeability as a function of liquid volume fraction. In this paper, a two-dimensional finite element program was developed for solving the temperature, velocity, and composition distributions simultaneously using the temperature recovery method. Several numerical examples demonstrate the capability and usage of the developed finite element program.