We consider the zero-viscosity limit of the 2D steady Navier-Stokes equations in $(0,L)\times\R^+$ with non-slip boundary conditions. By estimating the stream-function of the remainder, we justify the validity of the Prandtl boundary layer expansion in shear Euler flow with some monotonicity assumptions on the solution of Prandtl's systems and some non-shear Euler flow cases.