A linear shear flow is present in a fluid along one side of a fixed wall; the fluid on the other side is at rest. However, when there is a slit or a hole in the wall, then the shear flow will induce a motion in the fluid on the second side through a shearing force across the gap. We consider the Stokes flow behaviour for such a phenomenon in a number of different geometries, with particular interest in the singular solutions generated when the width of the slit, or size of the hole, is small.