Dynamically consistent global models of mantle convection with plates are developed that are consistent with detailed constraints on the state of stress and strain rate from deep focus earthquakes. Models that best fit plateness criteria and plate motion data have strong slabs that have high stresses. The regions containing the MW 8.3 Bolivia and MW 7.6 Tonga 1994 events are considered in detail. Modeled stress orientations match stress patterns from earthquake focal mechanisms. A yield stress of at least 100 MPa is required to fit plate motions and matches the minimum stress requirement obtained from the stress drop for the Bolivia 1994 deep focus event. The minimum strain rate determined from seismic moment release in the Tonga slab provides an upper limit of ∼200 MPa on the strength in the slab.