The second normal stress difference N-2 experienced by non-Newtonian fluids flowing in a pipe may give rise to secondary flows in the transverse direction. As a result, one component tends to encapsulate the other in stratified flows. In multilayer coextrusion, such secondary flows tend to distort the interface and affect layer uniformity. This paper presents numerical simulations of the elastically driven encapsulation in two-component stratified viscoelastic fluids. The simulations are based on a phase-field theoretical model and use finite elements with adaptive meshing to resolve the moving interfaces. The results suggest two mechanisms for elastic encapsulation: One due to the mismatch of N-2 between the components and the other due to noncircular geometry of the cross section. In circular pipes, the more elastic fluid tends to protrude into the other component in the center of the pipe and become encapsulated. This produces the curtate cycloid interface shape commonly seen in experiments. If the cross section is noncircular, both the geometric effect and the elastic stratification are at work, and the interfacial motion is determined by the competition of these two mechanisms. This understanding provides an explanation for the anomalous encapsulation of the less elastic component by the more elastic one observed in multilayer coextrusion. (C) 2008 The Society of Rheology.