We analyze shear waves from a 27 kiloton nuclear explosion at 597 m depth in salt at Azgir, Kazakhstan, and four subsequent small nuclear explosions in the water-filled cavity of the original explosion. We use local recordings on a common set of radial and vertical component instruments to identify the source of these shear waves. These small explosions caused minimal damage to the cavity walls and so are similar in some important ways to cavity decoupled explosions; however, the signal size is comparable to a tamped explosion. The shear wave amplitudes relative to P generated by the water-filled cavity explosions are comparable to each other and to the tamped explosion. Comparison of the water-filled cavity explosions’ P spectra with a distinct bubble pulse peak and two distinct S phases, which lack that spectral peak, indicates that the S phases are not scattered from P. The initial S-waves’ travel-time curve, impulsiveness, and compactness are consistent with generation at or very near the source and are inconsistent with significant scattering much outside the source volume. We estimate that the S waves are consistent with an S-wave source at the same depth and with the same moment as the spherical component of the explosion source. Nonlinear axisymmetric numerical modeling of the nonlinear deformation of the salt medium indicates that neither fracturing nor asphericity of the nonlinear region outside of the cavity, for a variety of source asymmetries, would produce the observed shear waves for any of the water-filled cavity explosions. Oscillations of the cavity itself due to variations in the amplitude and timing of the pressure around the cavity wall can, however, produce shear waves at the frequencies observed. Both offset of the source and asphericity of the cavity lead to such variations in pressure.