Compositional variation in initial growth was observed in Liquid Phase Epitaxy (LPE) experiments. It is thought that the cause is the flow of the melt which is induced by the slide of the entire melt from the place where there isn't substrate to the substrate before growth. The phenomenon was simulated with a one dimensional model in InGaP growth with a convection term added to a diffusion-limited model. The velocity of flow in the melt was approximated to Stokes's first problem. It was shown that composition of In in grown solid with the flow is larger than that without the flow. In this paper, InGaP LPE growth is considered and a two dimensional model of the flow is used. For the solute transport, a two dimensional model is also adopted except at the growth interface. A result similar to the one dimensional model was obtained. In the two dimensional model, In composition is greater than that in the case without flow for the greater part of the growth time, but decreases when the flow transports dilute solution. This decrease doesn't appear in the one dimensional model. This phenomenon can be explained by considering the influence of the flow on the mole fraction near the boundary layer.