The viscous behaviour of concentrated suspensions of solid particles in non-Newtonian power-law fluids is discussed here. After a brief review of the existing models, new models are presented for the constant shear-rate relative viscosity of concentrated suspensions with power-law matrices. To validate the models, experimental work is carried out on the rheology of suspensions of glass beads in aqueous polymer solution using a controlled stress rheometer. The volume fraction of particles is varied from 0 to 44.9%. The experimentally measured flow curves of suspensions are described satisfactorily using the proposed models.