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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 (V(P)/V(S)) where there is coincident P-and S-wave ray coverage. We compare the two V(P) inverse velocity models to each other and to results from forward modeling, and we compare the V(S) inverse models. The V(S) and V(P)/VS models differ in structural details from the V(P) models. In particular, dipping, tabular zones of low V(S), or high V(P)/V(S), 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 V(S) versus V(P) 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 V(P) = 3 to 5 km/s (or V(S) similar to 1.25 to 2.9 km/s), where our refraction V(S) is lower by a few tenths of a kilometer per second from V(S) based on direct measurements. Our new V(S) - V(P) curve may be useful for modeling the lower limit of V(S) from a V(P) model in calculating strong motions from scenario earthquakes.