There is ongoing debate about the strength of lithosphere in different tectonic settings and whether related observations are consistent with laboratory-derived constitutive laws. For subduction zone flexure, different studies have answered this question with both yes and no, while recent work on seamount-related flexure seems to conclude definitely no. If classical models of lithospheric strength are incompatible with observations, can we determine whether the implied weakening relates to the brittle or ductile parts or the envelope (or both)? This study investigates stress distribution in the oceanic lithosphere as it bends and yields during subduction. Two main observational constraints are considered: the maximum bending moment that can be supported by the subducting lithosphere, and the inferred neutral plane depth in bending. We particularly focus on regions of old lithosphere where the apparent neutral plane depth is about 30 km. We use subduction modelling approaches to explore these flexural characteristics, including potential estimation errors. This motivates a reinterpretation of key data-sets, and demonstrates an important convergence of evidence for what we call an intermediate model of lithospheric strength: weaker than classical models, but stronger than some inferences at seamounts. We consider the non-uniqueness that arises due to the trade-offs in strength and background stress state, arriving at two main conclusions: 1) old lithosphere that exhibits a 30 km neutral plane depth is difficult to reconcile with moderate-to-high effective tension, of the magnitude often assumed to result from slab pull; 2) the assumption of moderate background compression provides a model that satisfies the flexural characteristics, while accommodating additional constraints such as the flow strength of dry olivine, and the friction coefficient inferred from seismological studies. An interesting outcome of this region in the parameter space, is that reverse faulting is predicted beneath the neutral plane at depths > 30 km.