AbstractA Lagrangian particle‐based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self‐compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non‐Newtonian fluids whose behaviour is described by a Bingham‐type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier–Stokes equations. The solution procedure uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence‐free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould‐filling behaviour. Copyright © 2010 John Wiley & Sons, Ltd.