In this paper a cross-slot geometry for which the height of the channel is small compared to the
other channel dimensions is considered. The normal components of the viscoelastic stresses are found
analytically for a second order fluid up to numerical inversion. The validity of the theoretical analysis was
corroborated by comparison with numerical simulations based on a stabilized Galerkin least squares finite
element method using an Oldroyd B fluid. Close agreement was found between numerical predictions
and analytical results for Weissenberg numbers up to 0.2. An explicit expression is formulated for
viscoelastic parameters in terms of the variation and strength of the first normal stress difference around
the stagnation point. The analysis is generalized for the case where the inlet channel width is different
from the outlet channel width. For such configurations it was found that uniformity of the elongation rate
was reduced
