The free (or open) boundary condition (FBC, OBC) was proposed by Papanastasiou et al. (A new outflow boundary condition, Int. J. Numer. Methods Fluids 14 (1992) 587-608) to handle truncated domains with synthetic boundaries where the outflow conditions are unknown. In the present work, implementation of the FBC has been extended to viscoelastic fluids governed by integral constitutive equations. As such we consider here the K-BKZ/PSM model, which also reduces to the upper-convected Maxwell fluid (UCM) for a single relaxation time and an appropriate choice of material parameters. The Finite Element Method (FEM) is used to provide numerical results in simple test cases, such as planar flow at an angle and Poiseuille flow in a tube where analytical solutions exist for checking purposes. Then previous numerical results obtained with the differential UCM model are checked in highly viscoelastic flows in a 4:1 contraction. Finally, the FBC is used with the K-BKZ/PSM model with data corresponding to a benchmark polymer melt (the IUPAC-LDPE melt). Particular emphasis is based on a non-zero second normal-stress difference, which has been reported in the literature to cause problems and seems responsible for earlier loss of convergence. The results with the FBC in short domains are in excellent agreement with those obtained from long domains used until now to accommodate the highly convective nature of the stresses in viscoelastic flows, for which the FBC seems most appropriate. (C) 2012 Elsevier B.V. All rights reserved.