Nine-component VSPs recorded in two wells 862 ft (263 m) apart in the Lost Hills oil field in the southern San Joaquin Valley of California show that the polarization of the faster shear (S) wave is aligned with the direction of maximum horizontal compressive stress as determined from analysis of tiltmeter data. Tiltmeters monitored fractures that were hydraulically induced in or near the VSP wells. When fractures were induced in a VSP well, fracture azimuths determined from tiltmeter data were N 53 degrees E and N 56 degrees E, respectively, in two different depth zones; in the same zones the polarization directions of the faster S-wave were N 58 degrees E and N 59 degrees E. When fractures were induced in a well 537 ft (164 m) from the other VSP well, tiltmeter data indicated a mean fracture strike of N 59 degrees E, while the polarization direction of the faster S-wave in that case was N 40 degrees E. The discrepancy between tiltmeter and S-wave polarization angles in this second case may correspond to differences in subsurface structures and horizontal stress directions between the two wells.S-wave polarization directions were determined by minimizing energy on off-diagonal components of the 2 X 2 S-wave data matrix, accomplished by computationally rotating sources and receivers. Although polarization directions obtained by assuming a homogeneous subsurface were moderately consistent with depth, considerable improvement in consistency resulted from analytically stripping off a thin near-surface layer whose fast S-wave polarization direction was about N 6 degrees E. S-wave birefringence for vertical travel averaged 3 percent in two zones, 200-700 ft and 1200-2100 ft (60-210 m and 370-640 m), which had closely similar S-wave polarizations. Between those zones, the polarization direction changed and the birefringence magnitude was not well defined. S-wave polarizations from two concentric rings of offset VSPs were consistent in azimuth with one another and with polarizations of the near offset VSP. This consistency argues strongly for the robustness of the S-wave polarization technique as applied in this area. The S-wave polarization pattern in offset data fits a model of vertical cracks striking N 55 degrees E in a weakly transversely isotropic matrix, where the infinite-fold symmetry axis of the matrix is tilted 10 degrees from the vertical towards N 70 degrees E. Such a model is of monoclinic symmetry.