In this study, we investigated the deformation behaviour of metal–graphene nanolayered composites for five face-centred cubic metals under compression using molecular dynamics simulations. It was found that by increasing the thickness of the individual metal layers, the composite strength increased, while the deformation mechanism changed from buckling to deformation twining in Cu, Au and Ag, which was absent in the monolithic form of those metals of the same orientation and size. The deformation twinning was found to be enabled by the graphene layer, which introduced pseudoelasticity and shape memory effects in the nanolayered membrane with more than ۱۵% recoverable compressive strain.