A numerical analysis of the time evolution of straight river channels is presented. The bed and bank, material is taken to be coarse, non-cohesive and uniform in size. As a result of the interaction of the flow and the bed, the cross-sectional shape of the river evolves in time toward a dynamic equilibrium shape. This equilibrium is characterized by constant width, vanishing sediment transport in the transverse direction, and small but non-vanishing streamwise transport rate of bed sediment. The model successfully describes the time relaxation of an initially trapezoidal channel toward the equilibrium shape, as evidenced by comparison with experimental data.