  In this paper, we consider the 2D second grade fluid past an obstacle
satisfying the standard non-slip boundary condition at the surface of the
obstacle. Second grade fluid model is a well-known non-Newtonian model, with
two parameters: $\alpha$ representing length-scale, while $\nu > 0$
corresponding to viscosity. We prove that, under the constraint condition $\nu
= {o}(\alpha^\frac{4}{3})$, the second grade fluid with a suitable initial
velocity converges to the Euler fluid as $\alpha$ tends to zero. Moreover, we
estimate the convergence rate of the solution of second grade fluid equations
to the one of Euler fluid equations as $\nu$ and $\alpha$ approach zero.
