This paper is devoted to the numerical study of the stability of the plane
flow for two immiscible fluids obeying Maxwell constitutive equation in a c
hannel of aspect ratio 8. For fixed viscosity and flow rate ratios, the sha
pe and non-linear behavior of interfacial waves induced by small perturbati
ons of the input flow rate are studied using finite element simulations for
various elasticity stratifications. The stationary flow, close to a Poiseu
ille flow and presenting a flat interface is first computed. Then the inter
facial wave generated by a pulse-like disturbance on entry flow rates is co
mputed by using time dependent computations. It takes the shape of a wave p
acket which is amplified or damped while moving towards the die exit. In un
stable cases, the maximum deviation increases with elasticity (the Weissenb
erg number). Interestingly, the elastic stratification between the two laye
rs can counteract unstable waves due to viscous stratification.