The propagation of vibrations in structures with some degree of extended disorder, i.e., departure from regularity or strict periodicity extended throtighout the structure, is discussed. An account is given of the phenomenon of normal mode localization, caused under certain circumstances by the disorder. This phenomenon means that vibrational energy injected into the structure by an external source cannot propagate to arbitrarily large distances, but is instead substantially confined to a region close to the source. Specifically, it is shown that the steady state response of the structure decays exponentially away from the source. This phenomenon, predicted by P.W. Anderson in 1958 with applications in solid state physics in mind, has been of great importance in understanding electrical conduction processes in disordered solids and can be very important in acoustical problems as well. In particular, it means that the literature on periodic structures can be misleading in a qualitative, and not just a quantitative, manner. The phenomenon is illustrated in terms of two simple mechanical models, a system of coupled pendula and a vibrating string or bending beam with mass and spring constraints.