The subsonic lifting surface theory due to H. Multhopp (Ref. 1) has been extended to include a chordwise discontinuity in the slope of the lifting surface, i.e. to include the effect of flaps, or ailerons. By representing the chordwise loading of a two-dimensional flapped flat plate in closed form, a new loading function is used in the L2 representation of the chordwise loading, and a new influence function k is defined. This function is dependent on the parameter ᴓh which describes the hinge position, and so the tabulation which has been done for the influence functions, i and j, in Multhopp’s original method have to be repeated for values of ᴓh. The method is restricted to linearized, non-viscous flow about thin wings of moderate aspect ratio of any planform. Values of lift, pitching moment and centre of pressure can be obtained across the span for deflected flaps, and the theoretical effect of planform can be studied. An example has been calculated for a straight rectangular wing of aspect ratio 6 with a full span 20% chord, trailing edge flap. A comparison with available experimental results shows that viscous effects are important in obtaining the correct magnitudes of lift and pitching moments.