One of the principal arguments for large stress differences in the lithosphere comes from the modeling of the deflection of the ocean lithosphere under seamount loads. Most published models indicate maximum stress differences of 2--3 kbar per kilometer of deflection, and maximum values approach 10 kbar. Geophysical support for the elastic plate theory comes mainly from gravity, which requires a broad negative anomaly on the flanks of the actual seamount, although these anomalies are not very sensitive to the density structure of the crust of the density of the sediment fill-in or the extent of this fill-in. The stress in the plate, however, is sensitive to these parameters, and in consequence, gravity is not a reliable indicator of the stress state. The lithospheric flexure model has been examined in some detail to evaluate this stress dependence on crustal densities and rheology. The approximations inherent in the linear theory have also been investigated. The main conclusions are that the stress differences can be significantly reduced (1) by adopting a lower density for the sediment fill-in than the usual 2.8 g cm-3, (2) by introducing a depth-dependent nonelastic rheology, and (3) by introducing large-deflection theory for the larger loads. For large loads, such as Oahu Island discussed by Watts (1978), the maximum stress under the load can be reduced to about 2 kbar or less near the upper surface of the plate, and the maximum stress differences &sgr;rr--&sgr;zz need not exceed 1 kbar. The introduction of the nonelastic rheology results in a stress, temperature, and load duration dependence of the 'apparent' flexural rigidity; large loads, loads of long duration, or loads on a high-temperature lithosphere all result in a thinner apparent plate thickness than small loads, loads of short duration, or loads on a cool lithosphere, all other factors being equal.