Polymer mixing in two-roll mills is of considerable importance, especially for rubber compounds. In this research, we have evaluated the flow field in the cross-section of a two-roll mill device to study the distributive and dispersive aspects of the mixing process. The flow analysis in this problem comprises the determination of the free surface of the polymeric material and air, as well as the calculation of the velocity components and pressure values in both phases. The polymeric fluid, i.e. the rubber compound, and air have considerable different viscosity values. To consider the effect of the mentioned discontinuity on the flow field, a technique based on the finite element method (FEM) and the moving least-squares (MLS) method is developed. In this method, each phase is assumed as an independent flow domain with a communal boundary (the polymer/air interface). The results of the flow analysis based on the MLS aided FEM method (MLS-FEM) are employed to study the effect of the operating condition on the extent of the dispersive and the distributive mixing in a two-roll mill.