The local asymptotic behaviour is described for planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. Similar to the PTT model, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PIT, a weaker polymer stress singularity is obtained O(r-(((1-lambda 0)(3-lambda 0)/4))) with slightly thinner stress boundary layers of thickness O(r((3-lambda 0)/2)), where lambda(0) is the Newtonian flow field eigenvalue and r the radial distance from the corner. In the benchmark case of a 270 degrees corner, we thus have polymer stress singularities of O(r(-2/3)) for Oldroyd-B, O(r(-0.3286)) for PIT and O(r(-0.2796)) for Giesekus. The wall boundary layer thicknesses are O(r(4/3)) for Oldroyd-B, O(r(1.2278)) for Giesekus and O(r(1.1518)) for PIT. Similar to the PTT model, these results for the Giesekus model breakdown in both the limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit). (c) 2010 Elsevier B.V. All rights reserved.