Three-dimensional numerical simulation of coextrusion process of two immiscible polymers through a rectangular channel has been performed using the finite element method. The upper convected Maxwell (UCM) model and the Phan-Thien and Tanner (PTT) model were considered as viscoelastic constitutive equations. The elastic viscous stress splitting (EVSS) method was adopted to treat the viscoelastic stresses, and the streamline upwinding (SU) method was applied to avoid the failure of convergence at high elasticity. The problem arising from the ambiguous outlet boundary condition that has previously been used in the three-dimensional simulation of a viscoelastic coextrusion process could be avoided by introducing the open boundary condition (OBC) method. The abrupt change or deviation of contact line position near the outlet that was observed when the fully developed outlet boundary condition was applied could be clearly removed by using the OBC method. The effects of viscoelastic properties, such as the shear viscosity ratio, the elasticity, the second normal stress difference, and the extensional viscosity on the interface distortion, the interface curvature, and the degree of encapsulation along the downstream direction have been investigated. The shear viscosity ratio between the polymer melts was the controlling factor of the interface position and the encapsulation phenomena. The interface distortion seems to increase as the elasticity ratio increases under constant shear viscosity, even though it is not so large. The degree of encapsulation seems to increase with increasing the ratio of the second normal stress differences. The extensional viscosity had minor effect on the encapsulation phenomena. The second normal stress difference was found to have a great influence on the increasing of the degree of encapsulation along the downstream direction as compared to the effect of the first normal stress difference..