With the increased use of polymer composite materials in automotive and aerospace structures comes an increased need for nondestructive evaluation techniques to characterize material properties and to determine the material’s state of stress. One method for the evaluation of applied and residual stresses is acoustoelasticity, a technique based on the fact that as a material is stressed the longitudinal and shear wave speeds change. Acoustoelasticity has been successfully used in slightly anisotropic materials such as rolled aluminum plates [1]. In addition to studies with metals, early work in acoustoelasticity included measurements in homogeneous, isotropic polymers. Among the materials tested under applied pressure and temperature changes were polystyrene, Lucite [2], and polymethylmethacrylate [3]. Acoustoelasticity in fiber reinforced composites has not received much attention although ultrasonic waves have been used to measure the usual second order elastic constants of glass/epoxy and boron/epoxy by Zimmer and Cost [4] and Sachse [5], respectively. In both of these studies the wave length to fiber ratio was such that the composite was considered as a homogeneous orthotropic elastic material. With this same assumption Prosser [6] measured the second order and most of the third order elastic constants in a T300 graphite/5208 epoxy unidirectional composite.