An experimental investigation has been made of the settling behaviour of concentrated suspensions in viscoelastic polymer solutions, as a function of the fluid rheological properties. The sedimentation experiments examined a wide range of shear-thinning and viscoelastic behaviour (power-law index n range 0.2 -1.0 and relaxation time X range 0.1 -100 sec), using model suspensions of closely-sized glass beads. The experimental results were compared with four available theoretical models which are based on the fluid rheological properties. A new relationship is proposed, based on the single particle settling velocity, a critical solids volume fraction c* and the fluid rheological properties. The new relationship predicts two different settling regimes: fast-setting for low solids loading c ≤ c*, and slow-settling for high solids loading c ≥ c*. The new relationship simplifies to the well- established Richardson-Zaki correlation for sedimentation in Newtonian fluids.