Unusual mechanical properties of mechanical metamaterials are determined by their carefully designed and tightly controlled geometry at the macro- or nanoscale. We introduce a class of nanoscale mechanical metamaterials created by forming continuous corrugated plates out of ultrathin films. Using a periodic three-dimensional architecture characteristic of mechanical metamaterials, we fabricate free-standing plates up to 2 cm in size out of aluminium oxide films as thin as 25 nm. The plates are formed by atomic layer deposition of ultrathin alumina films on a lithographically patterned silicon wafer, followed by complete removal of the silicon substrate. Unlike unpatterned ultrathin films, which tend to warp or even roll up because of residual stress gradients, our plate metamaterials can be engineered to be extremely flat. They weigh as little as 0.1 g cm(-2) and have the ability to 'pop-back' to their original shape without damage even after undergoing multiple sharp bends of more than 90°.