Mechanical twinning of minerals is a deformation process that occurs to a first order under a critical resolved shear stress that is independent of temperature and strain rate. Thus unlike critical shear stresses for intracrystalline slip, extrapolations from laboratory measurements to the field situation are not necessary. The critical shear stress for twinning does not appear to be affected by hydrostatic pressure or by fluid pore pressure. Thus unlike the situation when coefficients of friction are used to infer stresses on faults, there need be no uncertainty in the shear stresses that caused twinning in nature, even if the depth of burial or the fluid pressure is unknown. Calcite, dolomite, and clinopyroxene are the rock-forming minerals with the greatest promise for the use of this technique to determine the magnitudes of paleobarsstresses. The critical shear stresses for calcite, dolomite, and clinopyroxene are about 100, 1000, and 1400 bars, respectively. These stresses are in an interesting range for helping resolve controversies concerning the magnitudes of stresses accompanying faulting. The method has not yet been used extensively, but in separate previous studies, differential stresses as high as 1250 and 2800 bars appear to have accompanied thrust faulting.