The analysis of stratified multiphase flow fields is difficult because the position of the interface is unknown a priori and there is a discontinuity in the normal viscous stress and/or pressure at the interface. A finite-element technique that uses double nodes along the interface has been implemented. The immiscible liquid displacement in a capillary tube was examined in detail. Fountain flow in the advancing fluid, reverse fountain flow in the receding fluid, and a recirculating flow region in the less viscous fluid were determined. In Newtonian flat film coextrusion the entry region, where the two immiscible fluids form an interface, and the characteristic swelling and bending of the extrudate at the die exit were studied. The computational results compare favorably with available experimental observations.