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 channel of aspect ratio 8. For fixed viscosity and flow rate ratios, the shape and non-linear behavior of interfacial waves induced by small perturbations of the input flow rate are studied using finite element simulations for various elasticity stratifications. The stationary flow, close to a Poiseuille flow and presenting a flat interface is first computed. Then the interfacial wave generated by a pulse-like disturbance on entry flow rates is computed by using time dependent computations. It takes the shape of a wave packet which is amplified or damped while moving towards the die exit. In unstable cases, the maximum deviation increases with elasticity (the Weissenberg number). Interestingly, the elastic stratification between the two layers can counteract unstable waves due to viscous stratification.