E. H. Dowell's linear theory of acoustoelasticity, which is capable of predicting the interior sound field for any structural model surrounding an arbitrarily shaped acoustic cavity subject to a prescribed internal sound source and/or external noise fields (or structural wall motion), has been employed. Using this theory, a method and associated computer program have been developed to compute the acoustic natural modes and natural frequencies of a cavity of arbitrary geometry. Comparisons of present calculated results and other theoretical and experimental values show generally good agreement. The theoretical model is also applied to predict the noise transmission through a single wall or a double wall/cavity system into a cavity. The effects of acoustoelastic and absorption couplings have been considered in a rigorous fashion. It is shown that a combination of added absorption material and a double wall/cavity system could significantly reduce interior noise levels.