In a slow linear shear flow over a cylinder in contact with a plane, there is an infinite set of eddies within the cusps at the point of contact. If the cylinder is not in contact with the plane, there is a flux of fluid between the cylinder and the plane, no matter how small the gap. When the gap is approximately 0·685 times the cylinder radius or less, the flow separates from the boundaries. Single eddies form alternately on the plane and the cylinder. These interlace as the cylinder approaches the plane and force the fluid which flows through the gap to take a tortuous path. The expressions for the force and torque acting on the cylinder are also given.