A general-purpose finite element program was used to simulate the swelling of multilayer polymer melts extruded concentrically from capillary dies; power-law constitutive models were considered. The interface and free surfaces were found iteratively by constructing streamlines. The pressure discontinuities across the interface were simulated numerically by double nodes to ensure continuity of velocities and stresses. A typical case of coextrusion with commercial polystyrene and high-density-polyethlene resins was studied and the results compared with experimental findings available in the literature.