The hydraulic transport of solid particles in a horizontal pipe is a well known practice in chemical plants and mining industry. The injection of gas into the flowing slurry results in a variety of flow patterns that affect the pressure gradient of the three-phase mixture in comparison with solid-liquid slurry flow. Furthermore, it may reduce or increase the pressure gradient relative to the conventional hydraulic transport of solids. This study constitutes the first attempt to formulate one-dimensional hydrodynamic models for evaluating the pressure gradients for stationary and moving solid beds overlaid by three-phase slug flow and for fully suspended three-phase slug flow of non-settling suspensions. The models for slug flow over stationary and moving beds are formulated by coupling the solid-liquid two-layer models of Doron et al. [1987. Slurry flow in horizontal pipes -experimental and modeling. International Journal of Multiphase Flow 13, 535-547] with a three-phase slug flow model. The proposed model for fully suspended three-phase slug flow constitutes an extension of the simple model for gas-liquid slug flow in horizontal pipes of Orell [2005. Experimental validation of a simple model for gas-liquid slug flow in horizontal pipes. Chemical Engineering Science 60, 1371-1381]. The proposed models, that are applicable to Newtonian slurries, were tested against the experimental data available in the literature over a wide range of operating conditions. In general, a good agreement was obtained between the predicted and experimental results. (C) 2007 Elsevier Ltd. All rights reserved.