Twelve three-component strong-motion displacement records are modeled for the 1979 Imperial Valley earthquake to recover the distribution of slip on the Imperial fault plane. The final model, for which point source responses are calculated by a discrete wavenumber/finite element technique, uses a structure with gradients in material properties rather than layers. The effects of a velocity gradient are investigated by comparing synthetics with a layer-over-a-half-space model using generalized rays. It is shown that a uniform fault rupture model on a rectangular fault plane does not explain the data. The preferred fault model has slip concentrated below 5 km (in the basement material) and between the epicenter (5 km south of the international border) and Highway 80. Within this region, there appears to be two localized areas of larger dislocations; one just north of the border near Bonds Corner and a second under Interstate 8 at Meloland Overpass. A major arrival associated with large amplitude vertical accelerations (up to 1.7 g) is identified in the El Centro array records. This arrival has an S-P time of approximately 2.3 sec at many of the array stations and is modeled as originating from a localized source 8 km to the south of the array. The moment is estimated to be 5.0 × 1025 dyne-cm from the strong-motion records, which is consistent with teleseismic body-wave estimates. The preferred fault model is strike-slip with a 90° dip. The average strike is 143°. However to explain vertical waveforms near the fault trace, a corrugated or wiggly fault plane is introduced. The average rupture velocity is in the range 2.5 to 2.7 km-sec (0.8 to 0.9 times the basement shear-wave velocity). The preferred model has unilateral rupture propagation to the north, although the data would allow a small amount of propagation to the south. The estimated stress drop for the entire fault plane is only 5 to 10 bars; however, the stress drop over the more localized sources is about 200 bars. The fault model is consistent with the pattern of seismicity and observations of aseismic creep in the Imperial Valley and suggests that the southern half of the Imperial fault acts as a locked section which breaks periodically.