The relationship of NDE with structural analysis is to provide quantitative information about material mechanical properties. For a composite structure (such as a rocket motor case) which is designed to handle in-plane loading, NDE should, ideally, provide information about the in-plane stiffness and strength properties of the structural material [1]. Because acoustic wave propagation depends on material elastic properties as well as being sensitive to material inhomogeneities, ultrasonic NDE has been nominated as a viable means of satisfying the needs of structural analytical modeling [2]. To address the need to detect in-plane properties, leaky Lamb wave [3,4] and non-normal incidence transmission [1] methods are being developed, for example. Development of composite ultrasonic NDE techniques, which are sensitive to material mechanical properties in the plane of a structure, required an understanding of acoustic wave propagation in anisotropic media. If a wave is introduced into the structure wall with an oblique angle of incidence less than critical angle, the refracted wave will travel in a non-principal or off-axis direction of the composite material. As a result, the wave energy will not generally travel in a direction normal to its phase fronts as it would in an isotropic medium. The acoustic wave energy or wave group propagates at a deviation angle, ψ, with respect to the phase front normal [5,6] as shown in Fig. 1. The deviation angle should be considered when measuring acoustic phase velocities from which the stiffnesses are calculated. The following sections discuss the effect of the group velocity propagation direction upon phase velocity measurements of quasi-longitudinal and quasi-shear waves propagating in non-principal directions in principal planes of orthotropic composite materials. Experimental results are shown for unidirectional graphite composite material samples.