When a fixed volume of a pure viscous fluid is squeezed between two parallel circular plates under a constant force, in the absence of surface tension, the radius of the propagating fluid front R increases such that R-8 is linear in time t in the lubrication limit [Engmann, J., C. Servais, and A. S. Burbridge, "Squeeze flow theory and applications to rheometry: A review," J. Non-Newtonian Fluid Mech. 132, 1-27 (2005)]. However, when the experiment is repeated with a suspension of rigid spheres instead of the pure viscous fluid, the behavior deviates from this R-8 vs t relationship at a radius R-m. This deviation is followed by the appearance of an instability in the azimuthal direction at the propagating suspension interface at a radius R-i. The instability arises due to the establishment of radial concentration and therefore viscosity gradients during the squeeze flow, which are susceptible to miscible viscous fingering [Tang, H., W. Grivas, D. Hometocovschi, J. Geer, and T. Singler, "Stability considerations associated with the meniscoid particle band at advancing interfaces in Hele-Shaw suspension flows," Phys. Rev. Lett. 85, 2112-2115 (2000)]. We experimentally determine the characteristic radii R-m and R-i for the converging parallel plate geometry and show that both radii scale as V-0(3)/a(2), where V-0 is the volume of the suspension loaded into the geometry before the experiment and a is the particle radius. This squeeze flow is identical to that produced in loading suspensions into the parallel plate viscometer and thus the concentration inhomogeneities identified here may play a role in the well known scatter of rheological measurements in this system. We also establish a critical parameter K, the ratio of R-m to the plate radius R-p, which can be used to predict the degree of homogeneity of the suspension upon loading. (C) 2010 The Society of Rheology. [DOI: 10.1122/1.3372837]