The purpose of this short note is to demonstrate that viscoelastic stresses are not necessarily smooth functions even in the absence of singularities in the flow geometries. Specifically, it is shown that, in general, the smoothness of stresses should be expected to deteriorate with increasing Weissenberg number if the flow has an interior stagnation point. The singularity exists not only at the stagnation point, but on the entire streamline downstream of this point. (c) 2006 Elsevier B.V. All rights reserved.