In this paper we present the results from a series of focus groups on the visualization of uncertainty in Equation-Of-State (EOS) models. The initial goal was to identify the most effective ways to present EOS uncertainty to analysts, code developers, and material modelers. Four prototype visualizations were developed to presented EOS surfaces in a three-dimensional, thermodynamic space. Focus group participants, primarily from Sandia National Laboratories, evaluated particular features of the various techniques for different use cases and discussed their individual workflow processes, experiences with other visualization tools, and the impact of uncertainty to their work. Related to our prototypes, we found the 3D presentations to be helpful for seeing a large amount of information at once and for a big-picture view; however, participants also desired relatively simple, two-dimensional graphics for better quantitative understanding, and because these plots are part of the existing visual language for material models. In addition to feedback on the prototypes, several themes and issues emerged that are as compelling as the original goal and will eventually serve as a starting point for further development of visualization and analysis tools. In particular, a distributed workflow centered around material models was identified. It was also found that users of material models contribute and extract information at different points in this workflow depending on their role, but encounter various institutional and technical barriers which restrict the flow of information. We expect the identification of this workflow, as well as the potential bottlenecks, to influence the development of visualizations to improve communication across this workflow and effectively express the uncertainties within the material models community.