In this paper two test cases adequate for the assessment of viscoelastic flow codes under unsteady flow conditions are investigated. For one of them an analytical solution is also derived. First, the start-up of planar Poiseuille flow between two parallel plates was tackled. For upper-convected Maxwell and Oldroyd-B models there exist analytical solutions making it possible to evaluate exactly the discretization errors of the transient numerical method. Good agreement was found between the present numerical results and those analytical solutions. especially for "shock" propagation. For the UCM fluid, small numerical oscillations were observed at points where the time derivative of velocity was discontinuous, but for the Oldroyd-B fluid a smooth development of the transient evolution was obtained. Results with the PTT model without solvent viscosity and the FENE fluids were also obtained and, as expected, the behaviour was similar to that found for the UCM and Oldroyd-B fluids, respectively. Then, a pulsating flow problem was studied. In this test case the flow is generated by a periodic pressure-gradient superimposed on a constant Poiseuille flow. The analytical solution for pulsatile Oldroyd-B flow in a channel was derived as part of the work and, again, difficulties in obtaining accurate numerical solutions with the UCM model were encountered, being necessary to employ extremely refined meshes. For the Oldroyd-B fluid no difficulties were found and the accuracy tended to improve with larger solvent viscosity parameter. (C) 2008 Elsevier BY. All rights reserved.