A one-dimensional transient mechanistic model of cuttings transport with conventional (incompressible) drilling fluids in horizontal wells has been developed. The model is solved numerically to predict cuttings bed height as a function of drilling fluid flow rate and theological characteristics (n, K), drilling rates, wellbore geometry and drill pipe eccentricity. The results of the sensitivity analysis showing the effects of various drilling operational parameters on the efficiency of solids transport are presented. The model developed in this study can be used to develop computer programs for practical design purposes to determine optimum drilling fluid rheology (n, K) and; flow rates required for drilling horizontal wells.