The mechanisms, distribution, and total moment of earthquakes within the bending oceanic plate seaward of trenches constrain possible mechanical models of the lithosphere. The average annual horizontal slip in normal fault earthquakes, as estmiated from the cumulative seismic moment, exceeds the total extension predicted by an elastic plate model. Thus bending is not predominantly an elastic process but must include a large amount of permanent deformation. Normal-faulting earthquakes are associated with every major trench system in the Pacific and Indian oceans, but events indicating horizontal compression are rare. The predominance of normal faults over thrust faults, normal events as deep as 25 km within the lithosphere (well constrained by pP), and the existence of large (Ms>7.5) normal fault earthquakes suggest that the average oceanic lithosphere is not under regional horizontal compressive stress which is a large fraction of the bending stresses. The location of thrust fault events as deep as 40--50 km, within the bendint plate requires the lithosphere to have significant strength at least as deep as 50 km. A two-layer plate model with elastic--perfectly plastic rheology can satisfy these seismological constraints and fit the observed shape of the trench and outer rise. Large regional stresses are not required, and variations in thickness and strength are not needed to fit individual profiles. In our preferred average model the mechanical plate is 50 km thick, with a weak (1-kbar yield strength) upper layer and a strong (6 kbar) lower layer. The mechanism for plastic strain at yield is assumed to be slip accompanying earthquakes. Normal fault earthquakes are consistent with Coulomb criterion failure, but some other failure mechanism must be invoked for the thrust fault earthquakes. The bottom of the plate is thought to be defined by a transition to steady state creep, induced either by increasing temperature with depth or by a change from dry to wet rheology. Variations in regional stresses should produce corresponding changes in the shapes of the topographic profiles. An examination of the tectonic settings of a number of profiles suggests that increasing horizontal compression should decrease the curvature of the profile in the vicinity of the zero-crossing point on the seaward wall of the trench.