Auxetics are materials that contract laterally when compressed, rather than expand, in contrast to common experience. Here we show that common metals and plastics can be rendered auxetic through the introduction of a regular array of holes. Under compression, these hard holey materials bypass localized failure modes, such as shear banding, and instead deform via a global pattern transformation previously reported in elastomeric structures. Despite significant variations in internal structure, the pattern transformation responsible for auxetic behaviour in both metals and plastics is governed by the elastic buckling of the slender struts that comprise the microarchitecture. Furthermore, in contrast to elastomeric structures, holey sheets made from hard materials exhibit significant negative post-buckling stiffness. This suggests that, beyond the geometrical nonlinearities associated with topological modifications, material nonlinearities which arise during plastic deformation offer further potential for altering the material properties of the constituent.