Self-cleansing is a hydraulic design concept for drainage systems for mitigation of sediment deposition. Experimental studies in the literature have mostly been performed in circular channels. In this study, experiments were conducted in five cross-section channels: trapezoidal, rectangular, circular, U-shape and V-bottom to investigate the non-deposition condition of sediment transport in rigid boundary channels. Deficiencies of conventional self-cleansing design based on a single value of velocity or shear stress and Camp criteria are highlighted in terms of channel cross-section shape; considering a higher number of hydraulic parameters, self-cleaning models are proposed for each cross-section channel; and finally, in order to make a general practical tool by incorporating a cross-section shape factor, a self-cleansing model is proposed to calculate the flow mean velocity at non-deposition conditions of sediment transport. The general self-cleaning model outperforms its alternatives when applying experimental data collected in this study and five datasets taken from the literature.