Abstract A review is made of the diffraction theory of the trailing edge noise generated by a flat-plate airfoil of zero-thickness and non-compact chord, according to which the sound is attributed to the scattering of a “frozen” pattern of turbulence wall pressure swept over the edge in the mean flow. Extension is made to determine the sound produced by very low Mach number flow over the edge of an airfoil of finite thickness. In applications it is desirable to represent the noise in terms of a surface integral over the airfoil involving a Green's function and a metric of the edge flow that can be calculated locally using the equations of motion of an incompressible fluid. It is argued that the appropriate metric for a rigid airfoil is the incompressible “upwash” velocity (determined by the Biot–Savart induction formula applied to the boundary layer vorticity outside the viscous sublayer), and not the surface pressure. Formulae for calculating the noise are given when the airfoil thickness is acoustically compact, and for both three- and two-dimensional edge flows. The theory is illustrated by a detailed discussion of a two-dimensional vortex flow over an airfoil with a rounded trailing edge. The problem is simple enough to be treated analytically, yet is also suitable for validating computational edge noise schemes.