In this study, a finite element model of a tissue-mimicking, viscoelastic phantom with a stiffer cylindrical inclusion subjected to an acoustic radiation force (ARF) is presented, and the resulting shear waves through the heterogeneous media are simulated, analyzed, and compared with experimental data. Six different models for the ARF were considered and compared. Each study used the same finite element model, but applied the following: (1) full radiation push; (2) focal region push; (3) single element focal point source; or (4) various thresholds of the full radiation push. For each case, displacements at discrete locations were determined and compared. The finite element simulation results for the full radiation push matched well with the experimental data with respect to replicating the shear wave speed and attenuation in the peak displacements through the background medium and inclusion, but did not illustrate comparable recovery after the peak displacements. As a result of this study, it has been shown that a focal region or point source push is not adequate to accurately model the effects of the full radiation push, but thresholding the full push can produce comparable results and reduce computation time.