The shear stress ?? that can be sustained by the rock mass in the environs of a mining-induced earthquake controls the near-fault peak ground velocity v of that event according to v???0.25(??/G) ??, where ?? is the shear wave speed and G is the modulus of rigidity. To estimate ?? at mining depths, I review the results of four studies involving Witwatersrand tremors that relate to the bulk shear strength. The first and most general analysis uses the common assumptions that the seismogenic crust is pervasively faulted, has hydrostatic pore pressure before mining, and an extensional stress state that is close to failure. Mining operations reduce the pore pressure to zero within the mine and redistribute the stresses such that, in localized regions, the state of stress is again at the point of failure. Laboratory friction experiments can be used to estimate ?? in the zero-pore-pressure regime. Second, model calculations of states of stress in the vicinity of milling at about 3 km depth indicated the shear stress available to cause faulting near the centre of a distribution of induced earthquakes. Third, laboratory experiments combined with microscopic analyses of fault gouge from the rupture zone of a mining-induced event provided an estimate of the average shear stress acting on the fault to cause this earthquake at a depth of 2 km. Fourth, moment tensors determined for mining- induced earthquakes usually show substantial implosive components, from which it is straightforward to estimate ??. These four different analyses yield estimates of ?? that fall in the range 30 to 61 MPa which implies that near-fault particle velocities could he as high as about 1.5 m/s. To the extent that the causative fault ruptures previously intact rock, both ?? and v, in localized regions, could be several times higher than 61 MPa and 1.5 m/s.