We present a foam flow model for flow pattern prediction in the polyurethane foaming process that considers the flow caused by foam expansion due to bubble generation. The flow pattern in the cavity is calculated by taking into account the initial volume shape and the rate of foam expansion of a poured reaction mixture. The validity of the model is investigated by applying it to the Hele-Shaw formulation, which assumes that the cavity is very thin compared to its width. The predicted flow patterns generally agree closely with experimental results measured in panel-type molds. A three-dimensional simulation is further developed based on the Stokes flow. The numerical formulation is performed by the control volume based-finite element method with an equal-order velocity-pressure formulation that does not exhibit spurious pressure modes. The flow patterns predicted by the three-dimensional simulation agree very closely with the experimental results. In particular, it clearly expresses the edge effect, in which the flow slows down at the edge, which is ignored in the Hele-Shaw formulation. This numerical simulation is suitable for rapid determination of the pouring position, volume of the mixture, and the air vent position.