The objective of this study was to develop a numerical model which predicts the geometry of an optimal straight stable channel for a given set of conditions: (1) the submerged coefficient of static friction of the channel bed material, (2) lift-to drag ratio, (3) grain size of the bed material, (4) water discharge, and (5) longitudinal slope of the channel. The term optimal stable channel refers to a channel capable of transporting sediment along a flat bed but whose banks are barely stable, i.e., all particles lying in the bank region are on the verge of motion. In addition to the geometry of the optimal stable channel, the model determines the critical and actual stress distributions along the perimeter of the channel cross-section. The model is based on the turbulent diffusion concept, which takes into account the diffusion of downstream momentum from the center of the channel towards its banks, due to Reynolds stresses. This causes a redistribution of stress along the channel perimeter. The resulting shear stress decreases monotonically as the lateral distance from the center of the channel increases. With such a distribution, it is possible for the stress to be above critical in the flat bed region, and below or at critical in the bank region. Thus, it allows for the coexistence of a mobile bed and stable banks; a phenomenon commonly observed in natural streams and laboratory flumes but not possible to explain on the basis of the threshold channel theory. Special attention is given to the area in the vicinity of the junction of the bed and bank, because of a discontinuity in the curvature of the bank profile that exists right at the junction point. This discontinuity, or step function, has been ignored by other researchers, although it can significantly influence the shape of the bank profile. A dirac delta function is used here for the third derivative in order to remedy the problem. By numerically integrating the third derivative, the change in the step function at the junction point can be determined. Regime relations are proposed based on numerical model calculations. The results of the numerical model compare favorably with existing laboratory and field data. It was found that the banks of an optimal stable channel are closely described by a fifth degree polynomial, which differs from the cosine, exponential, and parabolic profiles suggested by earlier investigators. It was also determined that the geometry of a threshold channel differs from that of a wide channel. / Master of Science