Paco posted a note from the OED on "beneath"/"under", a while ago:
The prepositional use of beneath seems originally to have been introduced to express the general notion of ‘lower than,’ as distinguished from the specific sense of under. But in process of time beneath was so largely used for under, that below was laid hold of to express the more general idea. In ordinary spoken English, under and below now cover the whole field (below tending naturally to overlap the territory of under), leaving beneath more or less as a literary and slightly archaic equivalent of both (in some senses), but especially of under. The only senses in which beneath is preferred are 'unworthy of' (‘beneath contempt’), and figurative uses in the sense of overwhelmed by or subject to (e.g. ‘to fall beneath the assaults of temptation’).
MrP