The condition of incipient motion and deposition are of the essential issues for the study of sediment transport. This phenomenon is of great importance to hydraulic engineers for designing sewers, drainage, as well as other rigid boundary channels. This is a study carried out with the objectives of describing the effect of cross-sectional shape on incipient motion and deposition of particles in rigid boundary channels. In this research work, the experimental data given by Loveless (1992) and Mohammadi (2005) are used. On the basis of the critical velocity approach, a new incipient motion equation for a V-shaped bottom channel and incipient deposition of sediment particles equations for rigid boundary channels having circular, rectangular, and U-shaped cross sections are obtained. New equations were compared to the other incipient motion equations. The result shows that the cross-sectional shape is an important factor for defining the minimum velocity for no-deposit particles. This study also distinguishes incipient motion of particles from incipient deposition for particles. The results may be useful for designing fixed bed channels with a limited deposition condition.