Non-isothermal calculation of flow history dependent viscoelastic stresses in a coextrusion die is performed using the 8-mode modified Leonov constitutive equation and the deformation rate field from finite element simulations. It is shown that a heuristic criterion based on the difference of normal stress differences across the layer interfaces in the merging area may be used to potentially detect the onset of interfacial instabilities. The developed technique can be a useful tool for coextrusion die design as well as for proper selection of materials and process conditions for coextrusion.