Shear Wave Elastography (SWE) is an ultrasound based technique which is able to measure tissue stiffness through the speed of induced shear waves. Tissue stiffness is often related to pathological conditions and detecting mechanical changes can help the recognition of potential diseases. The clinical use of SWE is limited to isotropic tissue due to the difficulty in assessing a theoretical model for more complex tissue and this project therefore aimed to evaluate the possibility of obtaining a full mechanical characterization of a transversely isotropic (TI) phantom with dual-probe SWE. A TI hydrogel phantom was developed and mechanical tests were performed to verify its anisotropy and determine the elastic moduli in both the perpendicular and longitudinal directions. Shear moduli were estimated using conventional and dual-probe SWE comparing the results to theoretical pure-transverse (PT) and quasi-transverse (QT) wave propagation modes. Both mechanical and SWE tests showed that the phantoms were transversely isotropic ET/EL=0.81. Moreover, multiple wave propagation modes calculated with dual-probe SWE showed a good agreement with the theoretical curves and indicated the possibility of measuring all the elasticity constants needed to fully characterize an incompressible, TI tissue with dual-probe SWE.