The equations of motion in conjunction with the free surface cell model have been solved numerically for the creeping flow of dilatant fluids through a fixed bed of spheres. The effect of the flow behaviour index (I less-than-or-equal-to n less-than-or-equal-to 2) on the individual as well as the total drag coefficients is elucidated. Finally, the theoretical predictions have been validated using the scant experimental results available in the literature.