Abs tractThe effective acoustic impedance matrix [Z(k)] is proposed and its applications are discussed.it is shown that [Z(k)] for any kind of multi-layered structures can be determined successively from the bottom substrate to the top layer. In addition, the use of [Z(k)] is able to avoid some problems often occurring in the numerical calculation for multi-layered structures. By using three typical examples, it is discussed how conveniently [Z(k)] is applied to characterise acoustic wave excitation and propagation in some complicated layered structures as well as in semiinfinite substrates.