A new impulse-response model for the edge diffraction from finite rigid or soft wedges is presented which is based on the exact Biot-Tolstoy solution. The new model is an extension of the work by Medwin et al. ͓H. Medwin et al., J. Acoust. Soc. Am. 72, 1005-1013 ͑1982͔͒, in that the concept of secondary edge sources is used. It is shown that analytical directivity functions for such edge sources can be derived and that they give the correct solution for the infinite wedge. These functions support the assumption for the first-order diffraction model suggested by Medwin et al. that the contributions to the impulse response from the two sides around the apex point are exactly identical. The analytical functions also indicate that Medwin's second-order diffraction model contains approximations which, however, might be of minor importance for most geometries. Access to analytical directivity functions makes it possible to derive explicit expressions for the first-and even second-order diffraction for certain geometries. An example of this is axisymmetric scattering from a thin circular rigid or soft disc, for which the new model gives first-order diffraction results within 0.20 dB of published reference frequency-domain results, and the second-order diffraction results also agree well with the reference results. Scattering from a rectangular plate is studied as well, and comparisons with published numerical results show that the new model gives accurate results. It is shown that the directivity functions can lead to efficient and accurate numerical implementations for first-and second-order diffraction.