Abstract: Based on the moving mesh scheme and the mixed finite element methods of EVSS/SU(elastic-viscous split stress/streamline upwind),a numerical simulation system of viscoelastic interfacial instability of polymer multiphase processing was establishedThe results of simulation showed a good agreement with the experimental data and theoretical calculation reported in literatureBy means of simulation, the effects of flow rate, viscosity and relaxation time of molten polymer on interfacial instability were investigated.It was found that the jumps in the first normal stress difference across the interface were the radical causes of interfacial instabilityThen the mechanism of interfacial instability was revealed, and several useful guiding principles for engineering practice were proposed.