The rheological behavior of suspensions containing cross-linked polymer particles (microgels) was studied. Under flow, these particles behave as soft spheres due to the shear-induced deformability of their external polymeric layer and the suspensions are strongly shear-thinning. At concentrations where particles are densely packed, the suspensions present a solidlike behavior involving elasticity and yield stress. The rheological modeling of such suspensions was based on the concept of the effective volume fraction of particles, which depends on hydrodynamic forces. In this sense, microgel particles were assumed to have a simple core−shell configuration and to interact through a repulsive polymer−polymer potential. The viscosity equation resulting from the modeling allows: (a) appropriate correlation of the experimental data shear stress versus shear rate in steady shear flow and (b) accounting for the softness of particles, which changes with concentration and shear stress. Also the predictions of the m...