The overflow fusion process is an important method for the manufacture of glass sheets and is currently used for the production of TFT/LCD display devices. The design of the forming apparatus is critical for obtaining very high surface quality glass to allow the successful application of semiconductor type materials. However, there is only little work presented in the literature, because of difficulties and expansions in experiments. This study outlines a numerical model for simulation of molten glass flow through an isopipe during the overflow fusion process. An explicit finite difference algorithm with the surface tracking method is proposed. The effect of the geometry of the forming apparatus, flow rate and viscosity of molten glass on the flow patterns during overflow was investigated. It was found that the stability and flatness of the sheet glass was influenced by the design of the forming apparatus, and the flow rate and viscosity of molten glass flow.