The reverberant shear wave (RSW) technique offers a promising framework for elastography. In this study, to characterize fibrotic fatty livers at different fibrotic stages, we employed an autocorrelation (AC) estimator within the RSW framework to evaluate shear wave speed (SWS) of viscoelastic media. To this end, we utilized both simulation and experimental approaches and excited the RSW field in a medium within each approach at the frequency of 150 Hz: (i) the finite element (FE) simulation of a RSW field in a 3D model of a whole organ fatty liver and (ii) the RSW experiments on two castoroil- in-gelatin phantoms fabricated in the lab. In the FE simulations, to represent a more realistic liver model, a thin adipose fat layer and a muscle layer were added as viscoelastic power-law materials on top of the liver model. The SWS estimation from the RSW simulation was compared with predictions from the theory of composite media for verification. For the RSW experiments on phantoms, the SWS estimations were compared with the SWS results obtained from performing the stress relaxation test as an independent modality. The simulation results showed that the RSW-based AC estimator provides good estimates of SWS, within >90% accuracy compared with theory. Also, the RSW estimator results from the phantom experiments at different background stiffness levels provided some experimental support for the utility of the RSW estimator. These results demonstrated that the AC estimator is sensitive to the changes in viscoelastic properties of viscoelastic media.