It is well accepted that the lithosphere may exhibit nonzero mechanical strength over geological time and space scales, associated with the existence of non-lithostatic (deviatoric) stress. The parameter that characterizes the apparent strength of the lithosphere is the flexural rigidity D, which is commonly expressed through the effective elastic thickness (T-e) of the lithosphere. Estimates of T-e for oceanic lithosphere approximately follow the depth to a specific isotherm (similar to 600 degrees C), which marks the base of the mechanical lithosphere. The physical meaning and significance of the effective elastic thickness for continents are still enigmatic, because for continental lithosphere estimates of T-e bear little relation to specific geological or physical boundaries. Although high observed values of T-e (70-90 km for cratons) can be partly explained by the present-day temperature gradients, the low values (10-20 km), in general, cannot. In addition, the elastic plate models are self-inconsistent in that they mostly predict intraplate stresses high enough to lead to inelastic (brittle or ductile) deformation, according to data of rock mechanics. To provide a basis for a physically consistent unified interpretation of the observed variations of T-e for continental and oceanic lithosphere, we developed an analytical and numerical approach that allows direct treatment of T-e in terms of the lithospheric theology, thermal structure, and strain/stress distribution. Our technique is based on finding true inelastic and equivalent (effective) elastic solutions for the problem of deformation of the lithosphere with realistic brittle-elasto-ductile theology. We show that the thermal state (thermotectonic age) of the lithosphere is only one of at least three equally important properties that determine apparent values of T-e. These other properties are the state of the crust-mantle interface (decoupling of crust and mantle), the thickness and proportions of the mechanically competent crust and mantle, and the local curvature of the plate, which is directly related to the bending stresses. The thickness of the mechanically competent crust and the degree of coupling or decoupling is generally controlled by composition of the upper and lower crust, total thickness of the crust, and by the crustal geotherm. Lf decoupling takes place, it permits as much as 50% decrease of T-e, compared with T-e implied from conventional thermal profiles. Comparison of the theoretically predicted T-e with inferred values for different regions suggests that the lower crust of most continental plates has a low-temperature activation theology (such as quartz) which permits crust and mantle decoupling. The curvature of the plate depends on the theological structure and on the distribution of external loads applied to the plate (e.g., surface topography, sediment fill, and plate-boundary forces). Bending stresses created by major mountain belts are large enough to cause inelastic deformation (brittle failure and a ductile flow) in the underlying plate, which, in turn, leads to a 30 to 80% decrease of T-e beneath such belts and less beneath the adjacent regions. The boundary farces and moments (e.g., due to the slab pull, etc.) lead to more localized but even stronger reductions in T-e (e.g., plate necking in subduction zones). Our approach provides a feedback between the ''observed'' T-e and theology, allowing to constrain the lithospheric structure from estimates of T-e.
