The Free (or Open) Boundary Condition (FBC, OBC) was proposed by Papanastasiou et al. (A new outflow boundary condition, Int. J. Numer. Meth. 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 tested also at inflow boundaries in several test problems of viscous or viscoelastic flow. The Finite Element Method (FEM) is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal or non-isothermal, steady-state conditions for Newtonian and non-Newtonian fluids. The present results extend previous ones regarding the applicability of the FBC, since they convincingly show that the FBC can be used equally well at inflow boundaries, without having to resort to artificially set inlet profiles for a given flow rate. (C) 2012 Elsevier B.V. All rights reserved.