Seismically derived depth estimates to the top of the ocean crust beneath the Hawaiian Islands indicate that the curvature of the deflected lithosphere is much larger than commonly believed. The conservative and model--independent curvature estimates exceed 10-7 m-1 and are comparable in magnitude to curvatures at trenches and outer rise systems. The depth estimates are used to constrain both two-dimensional (2-D) and three-dimensional (3-D) flexural models. The curvature constraints require a 2-D variable elastic thickness that decreases from 35 km in areas away from the volcanic load to 25 km directly beneath the load. In an attempt to understand the nature of the yielding beneath the Hawaiian Islands we introduce two new 3-D models. The first model combines a realistic yield strength based rheology with a new technique for 3-D flexure calculations in which the elastic plate thickness is curvature--dependent. The new variable rigidity model predicts an undeformed (mechanical) plate thickness of 44 km, decreasing to 33 km beneath the big island of Hawaii. The best-fitting mechanical thickness corresponds approximately to the depth to the 600 ¿C isotherm in 90-m.y.-old lithosphere. The second model uses a broken plate, but here the crack is oriented along the weak Molokai fracture zone rather than along the island chain trend. This unconventional flexure model can explain the observed asymmetry in the depth data across the fracture zone without requiring the excessively large elastic thickness of more conventional broken plate models. Both the proposed models imply that modeling with constant thickness plates may underestimate the true mechanical plate thickness by being unduly influenced by the weak zone beneath the seamounts. ¿ American Geophysical Union 1993