The effect of the operation of a 15 per cent trailing edge control surface on the flow around a two-dimensional aerofoil in a high subsonic shock-free condition is investigated using the integral equation method developed by Nixon and Hancock. The effect of retaining the non-linearities in the transonic potential equation is to increase considerably the magnitude of the pressures over the front part of the aerofoil in comparison with the pressure found using a modified linearised theory in which significant second-order terms in the boundary conditions are retained. The magnitude of the lift coefficient and the pitching moment coefficient are increased by 10-15 per cent over the values found using the modified linear theory, and by 20 per cent over the values found using standard linear theory. However, the magnitude of the hinge-moment coefficient is decreased by the order of 20 per cent compared with the modified linear values and by 30 per cent when compared to the standard linear values.