We use a phase-field model to simulate displacement flow between a Newtonian and a viscoelastic fluid in a two-dimensional channel. The viscoelastic fluid is described by the Oldroyd-B model and the stress singularity at the contact line is regularized by the Cahn-Hilliard diffusion. In a small region near the contact line, the flow field features a large shear rate that produces a high polymer stress even at relatively low wetting speed. This polymer stress pulls the interface toward the viscoelastic fluid. As a result, the viscous bending at the contact line is enhanced when the advancing fluid is viscoelastic and weakened when the receding fluid is viscoelastic. However, the overall effect is limited by the small size of this strong shear region. These results are consistent with experimental observations. By examining the flow and stress field in the neighborhood of the contact line, we find that viscoelastic stress growth within a finite residence time provides a plausible explanation of the curious experimental observation that the contact line is affected by the viscoelasticity of the oligomeric solvent rather than the high molecular-weight polymer solute. (c) 2012 Elsevier B.V. All rights reserved.