We present a 3-D finite element (FE) model of a novel hexagonal SAW device which finds applications in materials characterization as well as chemical and biological sensing. Prior to the device fabrication on any piezoelectric substrate, it is important to establish the type of waves that are generated along the various delay paths. The choice of a delay path for any specific application depends on the propagation characteristics of the wave generated along the crystal cut and orientation corresponding to that delay path. The frequency response as well as wave propagation characteristics along the three different delay paths corresponding to crystal orientation with Euler angles (0, 90, 90), (0, 90, 30) and (0, 90, 150) for a LiNbO3 substrate is analyzed using a FE model. 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 generate mixed wave modes with a prominent SH component whereas the (0, 90, 90) direction generates a Rayleigh wave. Our simulation results indicate that the hexagonal SAW device based on LiNbO3 can be utilized for rapid and simultaneous extraction of multiple film 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.