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Many cold-working processes for polycrystalline metals cause alignment of the grains with a single symmetry axis. This type of microstructure is called fiber texture. The existence of a preferred orientation of the grains has a significant influence on the propagation and scattering of ultrasonic waves, which are often used for material inspection. Knowledge of the wave attenuation of such textured materials is of both theoretical and practical interest to nondestructive testing and materials characterization. In this article, the quantitative relations between fiber texture and wave attenuations of hexagonal crystals are presented. The texture is characterized by a Gaussian distribution function that contains a single parameter that governs the transition of the texture from perfectly aligned crystals to statistically isotropic. Under this assumption, the materials of interest have a varying degree of transverse isotropy representative of processing conditions. Simple expressions for the attenuations of the three modes of waves are given in a concise, generalized representation. Finally, numerical results are presented and discussed in terms of the directional, frequency, and texture dependence. The results presented are expected to improve the understanding of the microstructure evolution during thermomechanical processing.