We apply the method of discrete wavenumber representation of elastic wave fields of Bouchon and Aki (1977) to the computation of synthetic seismograms for an explosive source in a layered medium. The method is based on the representation of the source radiation by a superposition of plane waves propagating in discrete directions. This discretization is exact and results from a periodic arrangement of sources. The two-dimensional (2-D) and three-dimensional (3-D) problems are described, and some examples of calculation are presented. They show that very complex seismograms can be obtained for rather simple geologic structures.