Plane Couette flow of a Newtonian fluid is linearly stable with respect to linear disturbances and plane Poiseuille flow becomes linearly unstable when the critical Reynolds number exceeds Re-c = 11544. As the Couette component is increased in a plane Couette-Poiseuille flow, it is known that the flow becomes absolutely stable for wall velocities above a critical value. It is suspected that a similar stabilization occurs for viscoelastic fluids. In this paper we show numerically that the plane Couette-Poiseuille flow of Oldroyd-B and modified FENE Chilcott-Rallison fluids is stabilized at a critical wall velocity approximately 0.7 times the maximal velocity of the plane Poiseuille flow, independent of the elastic parameters investigated. This value is surprisingly close to the Newtonian critical value. A long wavelength analysis, following the distinguished limit method of Cowley and Smith 181, confirms that at leading order this stabilizing wall velocity is indeed independent of the elasticity number of the flow. (C) 2010 Elsevier B.V. All rights reserved.