Classical elasticity is surprisingly robust.

This paper was just published in Nano Letters.  The authors use suspended, single-layer graphene as a template for the growth (via atomic layer deposition) of aluminum oxide, Al₂O.  Then they use an oxygen plasma to etch away the graphene, leaving a suspended alumina membrane 1 nm thick.  This is very cute, but what I find truly remarkable is how well the elastic properties of that membrane are modeled by simple, continuum elasticity.  The authors can apply a pressure gradient across the membrane and measure the deformed shape of the membrane as the pressure difference causes it to bulge.  That shape agrees extremely well with a formula from continuum mechanics that just assumes some average density and elastic modulus for the material.  That's the point of continuum mechanics and elasticity:  You don't have to worry about the fact that the material is really made out of atoms; instead you assume it's smooth and continuous on arbitrary scales.  Still, it's impressive to me that this works so well even when the total thickness of the material is only a few atoms!