Structural details of the crust determined from P-wave velocity models can be improved with S-wave velocity models, and S-wave velocities are needed for model-based predictions of strong ground motion in southern California. We picked P- and S-wave travel times for refracted phases from explosive-source shots of the Los Angeles Region Seismic Experiment, Phase II (LARSE II); we developed refraction velocity models from these picks using two different inversion algorithms. For each inversion technique, we calculated ratios of P- to S-wave velocities (VP/VS) where there is coincident P- and S-wave ray coverage.We compare the two VP inverse velocity models to each other and to results from forward modeling, and we compare the VS inverse models. The VS and VP/VS models differ in structural details from the VP models. In particular, dipping, tabular zones of low VS, or high VP/VS, appear to define two fault zones in the central Transverse Ranges that could be parts of a positive flower structure to the San Andreas fault. These two zones are marginally resolved, but their presence in two independent models lends them some credibility. A plot of VS versus VP differs from recently published plots that are based on direct laboratory or down-hole sonic measurements. The difference in plots is most prominent in the range of VP = 3 to 5 km=s (or VS ~ 1:25 to 2:9 km/s), where our refraction VS is lower by a few tenths of a kilometer per second from VS based on direct measurements. Our new VS - VP curve may be useful for modeling the lower limit of VS from a VP model in calculating strong motions from scenario earthquakes.