Anisotropy in crustal seismic wave propagation is a well-documented phenomenon. There are several proposed causes; the cause at any specific site must be determined by local geology. The presence of anisotropy can be identified by shear-wave splitting, when shear-wave arrival times are slightly offset due to different travel speeds. When simulating anisotropy, a common simplification is that of transverse isotropy (TI). By simulating anisotropy in a general case, new insights may be gained. The goal of this research was to model seismic anisotropy using TI and observer shear-wave splitting. A finite element scheme was used to implement the TI model. Anisotropy was introduced in the vertical direction in the form of a slowed shear-wave velocity. The seismic source was a Gaussian pulse. By visualizing discrete timesteps during the simulated propagation, a non-uniform wave front was detected. This deformed wave front was most prominent in the z-velocities. Comparison to isotropic wave fronts illustrate the differences. Another method of visualization is the seismogram. A synthetic seismogram on the surface of the model clearly showed the difference in shear-wave speeds. Rotating the seismogram in the radial, SV and SH coordinates showed similar results. Observational data from a seismogram in southern California shows a real case of shear-wave splitting. The results indicate that the model worked as planned. Shear-wave splitting was observed by two methods of visualization. Though the model is basic, it can be expanded in complexity and scale to bring its realism and relevance to a higher level.