Tissues such as skeletal muscle and kidneys have well-defined structure that affects the measurements of mechanical properties. As an approach to characterize the material properties of these tissues, different groups have assumed that they are transversely isotropic (TI) and measure the shear wave velocity as it varies with angle with respect to the structural architecture of the organ. To refine measurements in these organs, it is desirable to have tissue mimicking phantoms that exhibit similar anisotropic characteristics. Some approaches involve embedding fibers into a material matrix. However, if a homogeneous solid is under compression due to a static stress, an acoustoelastic effect can manifest which makes the measured wave velocities change with the compression stress. We propose to exploit this characteristic to demonstrate that stressed tissue mimicking phantoms can be characterized as a TI material. We tested four gelatin phantoms made with different concentrations of gelatin. Stress was applied by the weight of a water container centered on top of a plate on top of the phantom. A linear array transducer and a V-1 Verasonics system (Verasonics, Inc., Redmond, WA) were used to induce and measure shear waves in the phantoms. The shear wave motion was measured using a compound plane wave imaging technique and applying autocorrelation to the received in-phase/quadrature data. The shear wave velocity, c, was estimated using a Radon transform method. The transducer was mounted on a rotating stage so measurements were made every 10° over a range of 0-360°, where the stress is applied along 0-180° direction. The shear moduli were estimated. A TI model was fit to the data and the fractional anisotropy was evaluated. This approach can be used to explore many configurations of transverse isotropy with the same phantom, simply by applying stress to the tissue mimicking phantom.