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A set of governing equations for flows in the vegetated domain has been derived with the assumption that the vegetation is of straight and rigid cylinder. The effect of vegetation on flow motion is represented by the additional inertial and drag forces exerted by the vegetation on the ambient flow. The derived governing equations are incorporated into an existing 3D turbulent free surface flow model. The new model is validated by available experimental data for open channel flows passing through the vegetation with different vegetation size and density. The numerical results agree very well to the experiment data.