The finite-difference method is used to propagate elastic waves through a 3-D model of the Santa Clara Valley, an alluvium-filled basin that underlies the city of San Jose, California. The model was based on depth to bedrock information from water wells in the area. The simulation corresponded to a region 30 (east-west) by 22 (north-south) by 6 (depth) km and contained about 4 million grid points. Synthetic seismograms from the simulation are accurate at frequencies up to 1 Hz. Motions from a magnitude 4.4 aftershock of the Loma Prieta earthquake were modeled. Snapshots of ground motion and synthetic seismograms from the simulation are presented. The simulation illustrates S-to-surface-wave conversion at the edges of the basin and the large amplitude and long duration of ground motion in the basin compared to the surrounding rock. Love waves produced at the edge of the basin are the largest arrivals in the transverse synthetics. Because of the slow group velocity of the Love waves, sites near the center of the basin have longer durations of significant motions than basin sites near the valley edges. Sites near the center of the basin also show larger peak amplitudes on the transverse component. Array analysis of the synthetic seismograms indicates that Love waves tend to propagate parallel to the eastern and western edges of the valley. Rayleigh waves are produced along the southern margin of the basin from incident S waves. Large radial motions occur where a Rayleigh wave impinges on the northeast margin of the valley. Some Rayleigh waves travel westward across the basin, after being scattered from the eastern edge of the valley. Synthetic seismograms from the simulation have similar peak amplitudes as seismograms recorded by the Sunnyvale dense array for this aftershock, although the duration of the tranverse component is not matched by the synthetic seismogram, using this basin model. The simulation indicates that the Love waves observed on the actual seismograms were produced by conversion of incident S waves at the southern margin of the Santa Clara Valley. 2-D simulations show how the S-to-Love-wave conversion is affected by the angle of incidence of the S wave and the sharpness of the velocity transition between the alluvium and bedrock. As more accurate basin models are developed, 3-D simulations should become valuable for predicting ground motions in sedimentary basins for future large earthquakes.