A numerical model for the general description of the sediment-laden flow is developed based on an Euler-Euler approach of the two-phase turbulent flow theory. The basic equations of the model are the Reynolds averaged equations of motion for both the fluid and the sediment phase in addition to the Reynolds averaged continuity equations for the mixture and for the sediment phase. The fluid phase and the sediment phase are coupled through their interaction forces including resistance force, inertia force, and lift force. Turbulence closure of the fluid phase is based on the conventional k-epsilon model while an algebraic particle turbulence model is applied to the sediment phase. The numerical method is based on the modified SIMPLE scheme. The model is applied to the computation of saturated sediment-laden flows and also the non-equilibrium transport of sediment by unidirectional flows under simple erosion and simple deposition conditions. The numerical results are well verified by the available experimental data. The vertical velocity of the sediment phase is also shown to be in very good agreement with the fall velocity of the sediment particles, which strongly support the assumption of Rouse's diffusion theory for suspended sediment under steady state. (C) 2011 Elsevier Ltd. All rights reserved.