We present the generalization to three dimensions of the discrete wave number representation method of Bouchon and Aki (1977). The method is developed to study the near field of a three-dimensional seismic source embedded in a layered medium. The elastic wave fields are represented by a superposition of plane waves propagating in discrete directions. The discretization is exact and results from a periodic two-dimensional arrangement of sources. The accuracy of the method is checked, in the case of a rectangular dislocation source radiating in an infinite medium, by comparing the results obtained with Madariaga's (1978) exact solution. Examples of the calculation of strong ground motion produced by a thrust fault and a strike slip fault are presented.