New data on mantle viscosity variation and plate motions suggest that the author's previous theory for the forces driving and resisting plate tectonics needs revision. The flow in the mantle associated with plate movements probably pervades the whole mantle instead of being almost entirely in a thin asthenosphere at the top of it. The first task undertaken in this paper is a calculation of the viscous torque exerted on a hemispherical plate by a vertical point force in the mantle directly beneath the plate boundary. This prototype problem is simple enough, even with asthenosphere and mesosphere assigned different viscosities, to allow the computing to be done with a large number of terms of the relevant spherical harmonic series. It shows that forces in the lithosphere and asthenosphere are the major source of torques on plates, especially if the asthenosphere viscosity is low, and that truncating the series at a pre-assigned degree can seriously underestimate the effect of a force in the asthenosphere. These results are used as a guide to the approximations to adopt for more realistic boundary conditions, where accurate computing by the same method as the prototype problem would be too time-consuming to do. The second task is estimating the torques actually driving and resisting the motion of the Earth's plates. It includes a recalculation of the ‘ridge push’ driving mechanism which gives a zero resultant torque about the centre of the Earth, in agreement with Archimedes' principle but contrary to a recent conclusion of Davis & Solomon. The recalculation does not affect ‘slab-pull’, which still has a non-zero resultant, balanced mainly by a non-zero mean angular velocity of the plate system relative to the mean mesosphere (in which the ‘hot spots’ are assumed in this work to lie). This angular velocity agrees well with observational data, and gives a test of the approximations on data not used in deriving them. Misfits between driving and resisting torques are found for each plate. They are smaller for the present method than its best-fitting competitor. Conclusions common to both are that the ‘slab pull’ driving force must be appropriately weighted for age and speed, and that the most important resisting force is viscous resistance to shear flow under the whole area of the plate, not the localized friction at subduction zones which some earlier work had suggested.