By combining experiments performed on nanoribbons in situ within a high-resolution TEM with objective molecular dynamics simulations, we reveal common mechanisms in the bending response of few-layer-thick hexagonal boron nitride and graphene nanoribbons. Both materials are observed forming localized kinks in the fully reversible bending experiments. Microscopic simulations and theoretical analysis indicate platelike bending behavior prior to kinking, in spite of the possibility of interlayer sliding, and give the critical curvature for the kinking onset. This behavior is distinct from the rippling and kinking of multi- and single-wall nanotubes under bending. Our findings have implications for future study of nanoscale layered materials, including nanomechanical device design.