A global study of trench flexure was performed by simultaneously modeling 117 bathymetrie profiles (original depth soundings) and satellite‐derived gravity profiles. A thin, elastic plate flexure model was fit to each bathymetry/gravity profile by minimization of theL1norm. The six model parameters were regional depth, regional gravity, trench axis location, flexural wavelength, flexural amplitude, and lithospheric density. A regional tilt parameter was not required after correcting for age‐related trend using a new high‐resolution age map. Estimates of the density parameter confirm that most outer rises are uncompensated. We find that flexural wavelength is not an accurate estimate of plate thickness because of the high curvatures observed at a majority of trenches. As in previous studies, we find that the gravity data favor a longer‐wavelength flexure than the bathymetry data. A joint topography‐gravity modeling scheme and fit criteria are used to limit acceptable parameter values to models for which topography and gravity yield consistent results. Even after the elastic thicknesses are converted to mechanical thicknesses using the yield strength envelope model, residual scatter obscures the systematic increase of mechanical thickness with age; perhaps this reflects the combination of uncertainties inherent in estimating flexural wavelength, such as extreme inelastic bending and accumulated thermoelastic stress. The bending moment needed to support the trench and outer rise topography increases by a factor of 10 as lithospheric age increases from 20 to 150 Ma; this reflects the increase in saturation bending moment that the lithosphere can maintain. Using a stiff, dry‐olivine rheology, we find that the lithosphere of the GDH1 thermal model (Stein and Stein, 1992) is too hot and thin to maintain the observed bending moments. Moreover, the regional depth seaward of the oldest trenches (∼150 Ma) exceeds the GDH1 model depths b