A numerical model of the reaction injection molding process was developed to test front shape and flow approximations employed in previous models. The model was two‐dimensional and simulated the flow, reaction, and heat transfer in the typically long axial dimension and the typically small thickness dimension of a mold. The filling front shape and the velocity profiles in the filling fluid were determined by numerical solution of the momentum equation with the appropriate stress boundary conditions using the method of Patankar (1980). The predicted temperature and conversion results agreed with calculations assuming that the front was flat perpendicular to the flow and that a parabolic velocity profile existed behind the fountain flow region at the front. Thus, simple assumptions about front shape and velocity in the thin dimension of a reaction injection mold can be employed without significant loss of accuracy in modeling reaction injection molding.