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We present a 3-D coupled-field finite-element model of a novel hexagonal surface acoustic wave (SAW) device which finds applications in materials characterization, as well as in chemical and biological sensing. Calculated frequency response as well as wave propagation characteristics along the three different delay paths corresponding to crystal orientations with Euler angles (0, 90, 90), (0, 90, 30), and (0, 90, 150) for a LiNbO3 substrate are analyzed using this finite-element structural model. The transient response of the hexagonal SAW device upon application of an impulse electrical input at the transmitting interdigital transducer fingers is utilized to deduce its frequency response. The amplitude fields as well as displacement contours, generated in an AC analysis, along the SAW delay-line and substrate depth are analyzed and utilized to evaluate the wave propagation characteristics along the three propagation directions in this hexagonal SAW device. Our findings indicate that the acoustic waves generated in the three Euler directions are very different in character. The (0, 90, 30) and (0, 90, 150) directions have mixed modes with a prominent shear-horizontal component, whereas the (0, 90, 90) direction generates a Rayleigh wave. This allows the hexagonal device based on LiNbO3 to be used for rapid and simultaneous extraction of multiple parameters (film material density, Lame and shear modulii, sheet conductivity) of a thin-film material and achieve a more complete characterization in comparison to a conventional SAW device. Comparison of the simulation results with those obtained using perturbational models and experiments shows good agreement. This validation enables the consideration of such complicated device configurations for practical application, and allows for extending the developed models to analyze propagation characteristics in these SAW devices based on other bare and multilayered piezoelectric substrates prior to fabrica- - tion.