Ultrasound radiation force-based methods have the ability of estimating the tissue viscoelastic material properties. A limitation of the current methods exists when the estimation of the mechanical properties is performed under the assumption that the tissue is isotropic and homogeneous thus, neglecting the inherent anisotropy nature of certain tissues. To study the viscoelastic characteristics of this phenomenon in a laboratory setting, we created a transversely isotropic (TI) phantom incorporating fibrous material with preferential orientations embedded in tissue mimicking gelatin using two different concentrations (8%, 14%), and we studied a sample of ex vivo pork tenderloin in a saline bath at 30°C. Measurements were made in the TI phantoms and the excised sample of pork muscle at different angles by rotating the phantom with respect to the transducer, where 0° and 180° were defined along the fibers, and 90° and 270° across the fibers. Shear waves were generated and measured by a Verasonics ultrasound system equipped with a linear array transducer operating at 4.1 MHz center frequency. To estimate the shear elasticity (μ1) and viscosity (μ2), a Voigt model was fit to the shear wave dispersion curves of the phase velocity within the bandwidth of 100-700 Hz. The values for μ1 and μ2 for the fibrous phantom at both gelatin concentrations and the pork tenderloin, indicate that they are angularly dependent, and exhibit a TI behavior that can be studied using viscoelasticity measurements.