A general‐purpose finite element program has been used to simulate the flow of two immiscible viscous fluids extruded concentrically from a capillary and from an annular die. The interface and free surfaces are found iteratively by taking into consideration that these surfaces are streamlines. The pressure discontinuities across the interface have been simulated numerically by double nodes to ensure continuity of the stresses and the velocities. A range of viscosity ratios is studied for several cases of inner/outer diameter ratios of the fluids. Extrudate swell calculations show that for inelastic Newtonian fluids, shrinkage occurs when the less viscous layer encapsulates the more viscous, which is also the preferential configuration in coextrusion from long dies. Swelling occurs when the more viscous fluid wets the capillary wall. These results are in general agreement with Tanner's inelastic theory of extrudate swell. In flow from annular dies, bending of the extrudate stream occurs toward the more viscous component due to the viscosity mismatch. The present results reveal some important trends that can be expected in actual coextrusion operations, depending upon viscosity and feed ratios.