An approximate diffraction theory based on the Sommerfeld half-plane solution is developed. It is shown that, in certain regions, the electromagnetic field scattered (in the two-dimensional problem) by a perfectly conducting half-plane with plane waves incident can be conceived as arising from the flow of electric and magnetic currents along the edge of the half-plane. Thisedge-currentconcept is extended to the diffraction of normally incident plane waves by an aperture of arbitrary form in a thin, perfectly conducting screen of infinite extent.The approximation is for large apertures and is probably asymptotic. Interaction between the fields scattered by different parts of the screen is neglected in the present treatment.Expressions are obtained for the tangential electric field in the aperture in terms of these edge currents. The case of the circular aperture is studied in some detail, axial and aperture field distributions being derived and compared with the available experimental and theoretical data. Agreement with experiment and theory is fairly close, and improves with increase of the ratio of aperture radius to wavelength of incident radiation.