The free surface and zero vorticity cell models have been combined with the equations of motion to investigate numerically the steady flow of incompressible power-law (shear-thinning and shear-thickening) fluids across banks of long cylinders. The equations of motion in the stream function/vorticity formulation have been solved numerically using a second order accurate finite difference method to obtain extensive information on the behaviour of the drag coefficient, surface vorticity distribution, streamlines and iso-vorticity patterns, for high Reynolds numbers (Re = 50500) and using a wide range of power-law index (0.3 <= n <= 2.0), and porosity (0.4 <= e <= 0.9) values. The behaviour of the aforementioned parameters at low Reynolds numbers has also been investigated, and validated using theoretical and numerical work from the literature. The results reported here enable extension of the limits of creeping flow behaviour up to Re = 50 for fluids with highly shear-thickening characteristics under low porosity conditions.