Many tissues, such as muscle, kidney, and breast, are mechanically anisotropic. Appropriately exploited, mechanical anisotropy can be a clinically relevant target for noninvasive imaging. An imaging method's potential for interrogating mechanical anisotropy can be experimentally evaluated using tissue-mimicking materials, also known as phantoms. The objective of this work is to demonstrate the feasibility of constructing mechanically anisotropic phantoms using 3D-printed polylactic acid (PLA) fibers embedded in gelatin hydrogel or polyvinyl alcohol (PVA) cryogel. Four identical fiber sets were printed; two were embedded in gelatin and two in PVA. Acoustic Radiation Force Impulse (ARFI) imaging was performed on the constructed phantoms, with data acquisitions at 0°, 30°, 60°, and 90° concentric orientations, where 0° and 90° corresponded to the long-axis of the spatially asymmetric ARF excitation being aligned across and along the fibers, respectively. Degree of anisotropy (DoA) was calculated as the ratio of peak displacements achieved at 90° versus 0° orientations. While both gelatin and PVA embedded fibers demonstrated elastic anisotropy, DoA values were 32% higher in gelatin. These pilot experimental results demonstrate that phantoms constructed of 3D-printed PLA fibers embedded in gelatin or PVA exhibit mechanical anisotropy as assessed by ARFI ultrasound.