Shear flow over a square array of widely-spaced rods aligned with the flow is investigated using singularity methods to solve Stokes equation. The flow field is determined for various arrays occupying a fraction of a Couette channel, for solid volume fractions from 0.001 to 0.1. Flow penetration into an array is quantified by the slip velocity at the array edge. This velocity is much greater than when the flow is across the array but still less than the value predicted by the use of Brinkman's equation.