This thesis provides a general theory of the diffraction of ultrasonic waves. The theory is then used to find the apparent attenuation which would result if certain damage states (transverse cracks and delaminations) are introduced into a graphite/epoxy laminate through which the ultrasonic wave passes. and [0, ±45, 90]s) is presented which shows changes in the apparent attenuation of, about 1 dB. These changes generally occur at loads which correspond to the range predicted for the formation of the above mentioned damage. Though no exact correlation between theoretical and experimental results is given, the predicted changes in the attenuation for several simple and common damage states are well within the range of experimental values. It is hoped that the technique described herein can be further developed and used to detect the formation and growth of damage in composite specimens in regions not readily visible by conventional techniques. / Master of Science