An experimental study of the flow of phosphate mine tailings was carried out in order to characterize these suspensions of fine particles for pipeline transport. Rheological measurements with a rotating cylinder viscometer indicate a viscoplastic behaviour which can be represented by a Herschell-Bulkley or by a Casson model. The variation of the parameters of these models with solids concentration reveals a change in the behaviour at a concentration of 10 to 15%. The pressure drops were measured during flow in capillary tubes, in both laminar and turbulent regimes. The variation of the pressure drop coefficient (Fanning friction factor) as a function of the generalized Reynolds number confirms the validity of the employed rheological models. The results are in good agreement with measurements made in pipes of industrial size. The velocity profiles measured with a novel ultrasonic velocimeter demonstrate the influence of the rheological behaviour on the yield and wall stresses.