The field diffracted by an aperture of any shape is evaluated asymptotically for small wavelengths on the basis of several approximate diffraction theories. These are the Kirchhoff method, its two customary modifications, and W. Braunbek's new modification. In each case, a double integral over the aperture is evaluated asymptotically, and contributions from interior stationary points, edge stationary points, and corners of the edge are obtained. The contributions from points of each type, according to all the theories examined are exactly of the form recently deduced by J. B. Keller using his geometrical theory of diffraction. The edge stationary points and the corners correspond respectively to rays singly diffracted from edges and from corners. For edge‐diffracted rays the Braunbek diffraction coefficients alone coincide with those given by the geometrical theory of diffraction, but the Braunbek method does not apply to corner diffraction. None of these methods takes account of multiple diffraction as does the geometrical theory of diffraction.