A computer-based numerical model of turbidity current flow and sedimentation is presented that integrates geological observations with basic equations for fluid and sediment motion. The model quantifies those aspects of turbidity currents that make them different from better-understood fluvial processes, including water mixing across the upper flow boundary and the interactions between the suspended-sediment concentration and the flow dynamics and sedimentation. The model includes three numerical components: (1) a layer-averaged three-equation flow model for tracing downslope flow evolution using continuity and momentum equations, (2) a sedimentation/fluidization model for tracing sediment-size fractionation in sedimenting multicomponent suspensions and (3) a concentration-viscosity model for quantifying the changes in resistance of such suspensions toward fluid and sediment motion. The model traces the evolution of a model turbidity current in terms the layer-averaged flow velocity, flow thickness, sediment concentration distribution, and the rate of sedimentation and sediment size fractionation. It generates synthetic turbidites with downslope variations in thickness and grain-size structuring at each point along the flow path. This study represents an effort to evaluate quantitatively the effects of basin geometry, sediment supply and sediment properties on the mechanics of turbidity current flow and sedimentation and on the geometry and grain size characteristics of the resulting deposits.