A mathematical model developed earlier for the time-dependent circular tube flow of compressible polymer melts subject to pressure-dependent wall slip [Tang and Kalyon, J. Rheol 52, 507 - 525 (2008)] was applied to the tube flow of polymeric suspensions with rigid particles. The model relies on the apparent slip mechanism for suspension flow with the additional caveat that the polymeric binder slips at the wall according to a pressure-dependent wall slip condition. The numerical simulations of the tube flow of concentrated suspensions suggest that steady flow is generated when the flow boundary condition at the wall is a contiguous strong slip condition along the entire length of the tube wall. The findings of the simulations are consistent with the experimental flow curves and flow instability data collected on suspensions of a poly (dimethyl siloxane), which itself exhibits wall slip, compounded with rigid and hollow spherical particles in the 10 -40% by volume range. Increasing the concentration of rigid particles gives rise to the expansion of the range of flow rates over which the flow remains stable, as consistent with the experimental observations. (C) 2008 The Society of Rheology.