  In this paper, the steady creeping flow equations of a second grade fluid in
cartesian coordinates are considered; the equations involve a small parameter
related to the dimensionless non--Newtonian coefficient. According to a
recently introduced approach, the first order approximate Lie symmetries of the
equations are computed, some classes of approximately invariant solutions are
explicitly determined, and a boundary value problem is analyzed. The main aim
of the paper is methodological, and the considered mechanical model is used to
test the reliability of the procedure in a physically important application.
