Herein a simple phenomenological theory that involves an effective viscosity tensor is developed for the analysis and interpretation of spectroscopic data of through-thickness ultrasonic resonance. Under this theory, the attenuation of each mode of through-thickness stress waves is proportional to the square of the resonance frequency, which indicates that this theory may be adequate for covering attenuation due to dislocation damping, but not for attenuation due to grain scattering. Ultrasonic attenuation of through-thickness shear waves in sheet samples of a continuous-cast AA 5754 aluminum hot band and its O-temper counterpart was measured with resonance EMATs. The frequency range in question was from 2 to 10 MHz. For the hot band, the attenuation of the two shear modes was found to be predominantly proportional to the square of the frequency. The viscosity constant pertaining to the fast shear mode was about 3 times that of the slow shear mode, suggesting a highly anisotropic dislocation structure in the hot band.