A two-dimensional (vertical) flow model is developed to simulate open channel flow. The governing equations are solved without any depth averaging. Free surface movement is handled with the help of Arbitrary Lagrangian Eulerian Method. k−ϵ closure is employed to determine the turbulent eddy viscosity. Spatial discretization is done using linear 3-noded triangular elements. Galerkin method of weighted residuals is used to obtain weak form formulation. Navier-Stokes equations are solved by marching in time using Fractional Step Scheme. Continuity equation is replaced with a pressure Poisson equation. Supercritical flow and hydraulic jump are simulated to validate the flow code. Suspended sediment transport is modeled using an advection-diffusion transport equation for sediment concentration. Bed load transport is determined with the help of empirical correlations. The boundary condition at the bed is specified as a reference concentration. Sample problem involving bed erosion and deposition is solved.