Some simple mechanical models of subducted lithosphere, combined with observations of Benioff seismic zones, challenge some commonly accepted views of descending lithospheric slabs. The great thermal ineartia of slabs results in very large negative buoyancy forces, and phase changes may provide significant additional downward forces, but it is not clear what opposing forces are large enough to balance these. For slabs which do not penetrate beyond a depth of 650 km, the only reasonable possibilities seem to be frictional stresses of about 0.2 GPa (2 kbar) in shallow fault zones or viscous resistance from the surrounding mantle, which requires effective viscosities of at least 5¿1021 Pa s (5¿1022 P), significantly greater than viscosities inferred from post-glacial rebound. Although more deeply penetrating slabs might encounter additional resistance below 650 km depth, this resistance seems unlikely to be able to provide significant support for the slab since the slab would probably buckle, whether or not compressional stresses are limited by brittle or ductile yielding; in any case, the slab would probably only be supported episodically, if at all, and the results of buckling or fracture should be more evident in Benioff zones. Again the only reasonable alternatives seem to be large shallow frictional stresses or a high-viscosity upper mantle, which would slow the growth of buckling instabilities.