Suspensions of glass beads in a very viscous Newtonian fluid were subjected to constant-force squeeze flow between parallel disks of finite size. Pressure sensitive film was placed under the suspensions in order to record the normal stress distribution at the surface of the plates. Suspensions with low volume fractions exhibit qualitatively different normal stress distribution patterns than those with high concentrations, suggesting a change in the flow regime. At low concentrations, the normal stress distribution changes smoothly from a maximum at the center to ambient pressure at the edge of the plates. At high concentrations, the normal stress distribution exhibits a relatively small region of very high values near the center with a precipitous drop to very low values in the surrounding region. These results indicate that the models (such as the Herschel-Bulkley model) being used to describe the rheology of bulk molding compounds and other highly filled materials may be inappropriate, and that at high concentrations it may be helpful to model these materials as undergoing granular flow.