A two-dimensional model is developed for mold filling in Reaction Injection Molding using a Petrov-Galerkin finite-element method with free surface parameterization. Dependence of viscosity on the conversion and temperature is represented by the Castro-Macosko function. The model predicts the velocity, pressure, temperature, and conversion distributions with time during the filling stage of a rectangular mold. No a priori assumptions are made regarding the shape of the advancing flow front, or regarding any variables in the flow front region. The accuracy is further improved by using the Petrov-Galerkin formulation, rather than the Galerkin formulation. The results are presented for well-characterized polyurethane systems, for which reliable experimental data is available. The predictions of the model for the pressure rise are in excellent agreement with the experimental data (1) even close to the gel point. These refined predictions are expected to assist in estimating fiber orientation and bubble growth in the final RIM parts, in which the flow front region plays the most important role. Characterization of polyurethane/polyurea and polyurea materials is underway, and will be subsequently incorporated in the model.