Numerical simulation of nonisothermal viscoelastic flow through a 4 : 1 contraction die is carried out using the open boundary condition method along the outflow boundary. Upper convected Maxwell (UCM) model is used as a constitutive equation for the viscoelastic fluid and elastic viscous stress splitting (EVSS) formulation with streamline upwinding (SU) method is used to treat the convergence problem at high Weissenberg number. The validity of the open boundary condition method is tested on two meshes having different downstream lengths. In isothermal flow, the results obtained on the mesh having long downstream length using fully developed velocity boundary condition are in good agreement with those obtained on the mesh having short downstream length using the open boundary condition method. In the case of nonisothermal flow, the results obtained on both meshes using the open boundary condition method show almost the same profiles. In nonisothermal contraction flow, the velocity profile along the symmetry line shows more pronounced overshoot than in isothermal case due to the viscous heating. The shape of velocity profile at the outflow boundary is more flattened than parabolic profile in isothermal case with increasing flow rate. The level of normal and shear stresses along the downstream wall decreases in the flow direction due to the high viscous heating unlike the stresses in the isothermal flow. (C)1999 Elsevier Science B.V. All rights reserved.