  Oftentimes observed divergence of numerical solutions to benchmark flows of
the UCM viscoelastic fluid is a known and widely discussed issue. Some authors
consider such singularities 'invincible'. Following the previous research, the
article gives more arguments against this position, for which it considers two
typical flows with a stagnation point, often a place of the flows' singularity.
For the flow spread over a wall, as previously for the counterflows, numerical
and asymptotic analytical solutions are presented. Both kinds of flows turn out
regular in the stagnation points, in particular, for high Weissenberg numbers.
A good accordance is demonstrated between the analytical and numerical results.
