International audienceThis paper is concerned with the investigation of stratified flows of viscoelastic fluids by three-dimensional numerical simulation. The aim is to elucidate the mechanism behind the phenomenon of encapsulation in the coextrusion of polymer fluids in which one component progressively encapsulates the other along the coextrusion die. It is commonly accepted that the main reason for fluid encapsulation is the viscosity difference between the two components, since in most of the experiments, the less viscous fluid is observed to encapsulate the more viscous one. The occasional occurrence of the opposite case is usually explained as an effect of the elasticity difference between the fluids, which is responsible for a so-cal...