A method of constructing a concealing volume comprises constructing a plurality of concealing volume elements around a concealable volume. Each concealing volume element has a material parameter arranged to direct a propagating wave around the concealable volume. The material parameter can be refractive index, electrical permittivity and magnetic permittivity. The concealing volume can be a metamaterial. The concealing volume diverts incoming propagating waves such that outgoing propagating waves appear to be unperturbed to an observer.