Suspensions filled close to their maximum packing fraction present special challenges in their processing and in their rheological characterization. In this report, the literature in the area of dilatancy of concentrated suspensions is reviewed. Furthermore, the shear viscosity of a Newtonian polymeric liquid filled with 60 vol. percent of ammonium sulfate has been investigated. Both capillary and parallel disk torsional flows, were employed, spanning three decades in shear stress. Upon correction for slip, the suspension exhibited shear thinning at low shear stresses and shear thickening at higher shear stresses. Above a critical wall shear stress, the shear viscosity of the suspension increased unboundedly and the flow became pluglike with apparent slip at the wall. These findings have important ramifications in the processing of composites from such concentrated suspensions.