In this paper, we consider viscoelastic stresses T-11, T-12 and T-22 arising in the stagnation flow of a dilute polymer solution; in particular. we consider an upper convected Maxwell (UCM) fluid. We present exact solutions to the coupled partial differential equations describing the viscoelastic stresses and deduce the results for the stress T-22 of Becherer et al. [P. Becherer, A.N. Morozov, W. van Saarloos, Scaling of singular structures in extensional flow of dilute polymer solutions, J. Non-Newtonian Fluid Mech. 153 (2008) 183-190]. As we considered the viscoelastic stresses over two spatial variables, we are able to study the effect of variable boundary data at the inflow. As such. our results are applicable to a wider range of fluid flow problems. (C) 2009 Elsevier B.V. All rights reserved.