Non-isothermal calculation of flow history-dependent viscoelastic stresses in an annular coextrusion die is performed using the 8-mode modified Leonov constitutive equation and the deformation rate field from finite element simulations. The study shows how the recently proposed total normal stress difference (TNSD) sign criterion, which quantifies the relative stretching of coextruded layers across an interface, can be used to investigate the role of the die design and elongational viscosities of coextruded materials from the point of view of interfacial instability. It is shown that both the die geometry and the elongational strain hardening have a crucial effect on the interfacial wave instability.