Abstract: The stresses of the cohesionless solids flow in water-sedimentmixture is a difficulty in the solid-liquid two phase theory. On the basesof the expansion model, the kinetic theory, and the continuous media theory,the stress constitutive relation of cohesionless solids flow withconsideration of the coefficient of elastic collision restitution has beenobtained, which included the friction stress, the slide stress, and thecollision stress. A critical value (\tau _c / \tau _e < 0.02, \tau _c represents the time experienced by a given particle between two consecutivebinary collisions, \tau _e is the particle relaxation time) was applied tojudge whether the friction stress and the slide stress could be neglected. Asimulation of water-sediment flow in inclined chute was carried out toemploy the new stress constitutive relation, and the calculated result wasgood agreement with the experiment data.