It has been discovered through experiment that the slurries at Huayuankou on the Yellow River, Lianyuangang, Dmgang, Yangtze River estuary, Dunkerque of France, etc. all behave as the Bingham fluid with thixotropic properties as the sediment concentration is large. Consequently, the setting velocity of a sphere, the maximum diameter of non-setting sphere and the shear stress of incipient motion of cohesive sediment in the slurry change significantly with the duration of rest after the slurry is strongly agitated, Based on the above fact, the quantitative relationship between the shear stress of incipient motion of cohesive sediment and the factors of the sediment concentration, the particle size, the yield stress measured by the viscometer and the duration of rest after agitation(consolidation time), etc, has been developed, and good results have been obtained, The condition of incipient motion of non-cohesive sediment obtained by various investigators have also been transformed to the dimensionless critical shear stress θ. It is found that the various values of θ, in general, come between Einstein’s 0.0715 and Shamofu’s (Шамов) 0.0245.