Numerical simulation of coextrusion process of viscoelastic fluids within a die has been carried out. In the coextrusion process velocity profile at the outflow boundary is not known a priori, which makes it difficult to impose the proper boundary condition at the outflow boundary. This difficulty has been avoided by using the open boundary condition (OBC) method. In this study, elastic viscous stress splitting (EVSS) formulation with streamline upwind (SU) method has been used in the finite element method. In order to test the validity of the OBC method, comparison between the results of fully developed condition at the outlet and those of OBC has been made for a Newtonian fluid. In the case of upper convected Maxwell (UCM) fluid, the effect of outflow boundary condition on the interface position has been investigated by using two meshes having different downstream lengths. In both cases, the results with the OBC method showed reasonable interface shape. In particular, for the UCM fluid the interface shape calculated with OBC was independent of the downstream length, while the results with the zero traction condition showed oscillation of interface position close to the outlet. Viscosity difference was found to be more important than elasticity difference in determining the final interface position. However, the overshoot of interface position near the con-fluent point increased with elasticity.