The presence and progression of neuromuscular pathology, including spasticity, Duchenne’s muscular dystrophy and hyperthyroidism, has been correlated with changes in the intrinsic mechanical properties of skeletal muscle tissue. Tools for noninvasively measuring and monitoring these properties, such as Magnetic Resonance Elastography (MRE), could benefit basic research into understanding neuromuscular pathologies, as well as translational research to develop therapies, by providing a means of assessing and tracking their efficacy. Dynamic elastography methods for noninvasive measurement of tissue mechanical properties have been under development for nearly three decades. Much of the technological development to date, for both Ultrasound (US)-based and Magnetic Resonance Imaging (MRI)-based strategies, has been grounded in assumptions of local homogeneity and isotropy. Striated skeletal and cardiac muscle, as well as brain white matter and soft tissue in some other organ regions, exhibit a fibrous microstructure which entails heterogeneity and anisotropic response; as one seeks to improve the accuracy and resolution in mechanical property assessment, heterogeneity and anisotropy need to be accounted for in order to optimize both the dynamic elastography experimental protocol and the interpretation of the measurements. Advances in elastography methodology at every step have been aided by the use of tissue-mimicking phantoms. The aim of the present study was to develop and characterize a heterogeneous composite phantom design with uniform controllable anisotropic properties meant to be comparable to the frequency-dependent anisotropic properties of skeletal muscle. MRE experiments and computational finite element (FE) studies were conducted on a novel 3D-printed composite phantom design. The displacement maps obtained from simulation and experiment show the same elliptical shaped wavefronts elongated in the plane where the structure presents higher shear modulus. The model exhibits a degree of anisotropy in line with literature data from skeletal muscle tissue MRE experiments. FE simulations of the MRE experiments provide insight into proper interpretation of experimental measurements, and help to quantify the importance of heterogeneity in the anisotropic material at different scales.