The clinical use of elastography for monitoring fibrosis progression is challenged by the subtle changes in liver stiffness associated with early stage fibrosis, and the comparatively large variance of stiffness estimates provided by elastography. Single Tracking Location Shear Wave Elasticity Imaging (STL-SWEI) is an ultrasound elastography technique that was previously demonstrated to provide improved estimate precision compared to Multiple Tracking Location (MTL) SWEI. As a result of improved precision, it is reasonable to expect that STL-SWEI would provide improved ability to differentiate liver fibrosis stage compared to MTL-SWEI. However, this expectation has not been previously challenged rigorously. In this work, the performance of STL- and MTL-SWEI in the setting of a rat model of liver fibrosis is characterized and the advantages of STL-SWEI in staging fibrosis are explored. The purpose of this study is to determine what advantages, if any, arise from utilizing STL-SWEI instead of MTL-SWEI in the characterization of fibrotic liver. Thus, the ability of STL-SWEI to differentiate livers at various METAVIR fibrosis scores, for ex vivo, post-mortem measurements, is explored. In addition, we examine the effect of the common confounding factor of fluid versus solid boundary conditions in SWEI experiments. Sprague-Dawley rats are treated with carbon tetrachloride over several weeks to produce liver disease of varying severity. STL and MTL stiffness measurements were performed ex vivo and compared to the METAVIR score from histological analysis and the duration of treatment. A strong association was observed between liver stiffness and weeks of treatment with the liver toxin carbon tetrachloride. Direct comparison of STL- and MTL-SWEI measurements show no significant difference in ability to differentiate fibrosis stages based on SWEI image mean values. However, image interquartile range is greatly improved in the case of STL-SWEI imaging compared to MTL-SWEI at small beam spacings.