Propagation of ultrasound across a solid layer with equally spaced parallel interfaces is studied by using a transfer matrix method. For a layer with identical interfaces the propagation of ultrasound is governed by a dispersion relation, which displays passing and stopping bands in the frequency domain. For a layer with interfaces that have random deviations from mean interface properties, the Fürstenberg theorem and Monte Carlo simulation have been used to study propagation of ultrasound across the layer. It has been shown that at all frequencies there is an exponential decay in the amplitude of the transmitted wave. This decay, which increases with increasing frequency, defines a localization phenomenon, since wave motion will be confined to the insonified side of the layer.