1. The forces acting on the two-dimensional aerofoil in a bounded uniform stream have been found for a variety of cases, and in the present paper an attempt is made to extend the theory to include linear shear-flow. The special case of the symmetrical Joukowsky aerofoil in unbounded shear-flow has been solved by Tsien (6) using real-variable theory. A more satisfactory method is using complex-variable technique indicated in § 3, and is applicable to a more general shaped aerofoil. The effect on the lift and moment when a plane boundary is present is then considered. When the aerofoil is not too near the boundary, the lift and moment can be expanded in powers of the ratio of a typical length in the aerofoil to the height of the aerofoil above the boundary, by following exactly the technique used by Green (1) in a recent paper dealing with the same problem but with a uniform fluid flow. In the last section the limiting case of the flat plate touching the boundary with its trailing edge is discussed.