In this paper, a simple model is presented which predicts the ultrasonic frequency spectra for a broad class of layered composite materials having a finite number of laminas. This model predicts spectra for arrays of glass plates in water and these spectra are experimentally verified. Precisely regular spectra are predicted for single plates, while irregular spectra are predicted for all of the arrays studied. Results relating to nondestructive testing which have emerged from this investigation include methods for predicting spectra for layered composite materials and techniques for mapping small changes in the modulus and thickness of composite materials. Also discussed is the existence of forbidden frequency bands for which ultrasound transmission is strongly attenuated in thick layered composites.