The rheological behavior of a very concentrated suspension (76.5 vol %), which serves as a widely used solid rocket fuel simulant, was characterized employing both torsional and capillary flows. No comprehensive studies of the rheology of concentrated suspensions have been carried out previously at such a high solids content. The suspension exhibited shear thinning over the apparent shear rate range of 30–3000 s−1. Significant slip at the wall was observed in both torsional and capillary flows with the slip velocity increasing from about 0.001 mm/s at a shear stress of 4 Pa to as high as 60 mm/s at 100 kPa. A flow visualization technique was applied for the first time to determine the wall slip velocities in torsional flow directly, to also provide the true deformation rate and feedback on yielding. The contribution of the slip of the suspension at the wall to the volumetric flow rate in capillary flow was found to increase with decreasing shear stress, giving rise to plug flow at sufficiently low shear stress values. The observed plug flow is related to the shear‐thinning nature of the suspension and differs from the behavior of shear thickening suspensions, which may exhibit plug flow at high wall shear stress values, i.e., above a critical wall shear stress in capillary flow.