The magnitude of shear stress in the lithosphere is bounded from below by the apparent stress and stress drop during intraplate earthquakes. Apparent stresses and stress drops for a number of mid-plate earthquakes are calculated from the earthquake magnitude, SH wave amplitude spectra, and estimates of the length of the fault zone. Apparent stresses vary between 0.1 and 2 bars, if m b is used as a measure of seismic energy, and stress drops lie between 2 and 70 bars. There is no systematic difference in either apparent stress or stress drop between these intraplate events and typical plate boundary earthquakes. These bounds on intraplate shear stresses are consistent with the inference from current models of plate tectonic driving forces that regional stress differences in the plates are typically on the order of 100 bars. The highest stress drops measured for midplate earthquakes under this model represent nearly total release of local tectonic stress.