Theoreticians in soil mechanics have been pursuing a probabilistic approach to the factor of safety of an embankment or dam for the past 10 years. The motivation for this work is in contrast to the current practice of deterministically computing a factor of safety and treating it as an absolute with no regard to its inherent statistical variability. Basic to the probabilistic approach is the selection of an appropriate statistical model to represent the histogram or probability density function (pdf) of the factor of safety values. Rather than simply assuming which pdf is appropriate, the Bureau of Mines collected data at two waste disposal embankments for consideration. This report addresses three candidate models, using the techniques of nonlinear curve fitting, and identifies the "best" model. A propagation of error formula for estimating the variability of fellenius' factor of safety is also discussed.