We present a theoretical study of the ground motion produced by shallow dip slip faults near the source. The earthquake is modeled as a finite three-dimensional dislocation embedded in a layered medium, and the resulting surface displacement is computed at more than a thousand locations distributed all over the source region. By combining together all the seismograms obtained, the time history and spatial dependence of the strong ground motion can be inferred. Calculations are carried out by using for the source geometry the fault plane obtained for the San Fernando earthquake. Various crustal structures are considered. When the medium departs from a homogeneous half space, the ground displacement exhibits a high degree of complexity. This complexity increases when low-velocity layers are present. Two of the major findings of the study are the striking directivity effect of the propagating rupture on the surface motion and the large amplification of horizontal motions by sedimentary layers.