The paper describes a mathematical and physical modelling of flow of complex slurries in pipelines, i.e. a flow of slurries composed of solids covering a very broad range of particle sizes that overlaps more than one flow patterns – non-Newtonian, pseudohomogeneous, heterogeneous and fully-stratified. A typical examples are residual products (“tailings”) from mining industry with normal average particle sizes of 20 to 100 μm or more. Experimental results of flows of complex slurries composing of non-Newtonian carrier fluid and three fractions of glass particles in 50 mm pipe are presented. Depending on the particle size, particles show different flow patterns and therefore considerable differences in pressure drops. Fine particles tend behave as a homogeneous matter, while coarser particles exhibit heterogeneous behaviour and even coarser particles form a sliding bed. A mathematical 3-component predictive model for turbulent flow of complex slurries is presented based on well-established semi-empirical formulae developed originally for flows with Newtonian carrier. The predicted values of pressure drops show very reasonable agreement with experimental results and indicate suitability of the model for engineering practice.