An upper bound estimate of the vertical component of stress present at oceanic convergent zones is obtained by examining the flexural style of the downgoing plate. A least squares procedure is used to invert the equations governing the flexure of a thin elastic plate, yielding an estimate of the plate's rigidity, and the lateral distribution and magnitude of the vertical stress. The stress estimates obtained from the elastic plate model are upper bounds, since any anelasticity will tend to weaken the lithosphere and thus require a smaller load to produce the same flexural response. Analyses of the Mariana, Bonin, Kuril and Aleutian Trenches show that the stress inducing lithospheric flexure reaches a maximum of less than 20 MPa within a few kilometers arcward of the trench. In all but the Aleutian Trench, the load decays to less than 1 MPa within 60 km of the trench, well before the Benioff Zone dip steepens. The distance between the trench axis and the stress maximum, as well as the net force applied to the plate, increase with increasing convergence rate. The estimated stress profiles are consistent with a model in which the stress inducing flexure results from the collision of the two plates along a narrow zone of interplate coupling located 15 to 20 km arcward of the trench axis. The trenches studied do not require a large vertical load in the vicinity of the steep part of the Benioff Zone, indicating that the weight of the subducted slab does not contribute support to the trench/outer rise bathymetry. This requires the normal component of slab weight to be supported by the asthenosphere, allowing the remaining component of weight to act parallel to the plate axis.