Two models of the flow over and through an immersed, vegetated layer are examined to study the onset of instability waves across the layer and to assess the effect of mild variations in the mean flow and in the drag force exerted by the canopy onto the frequency and growth rate of the monami instability. One of the two models, based on the use of Darcy’s equation, with a tensorial permeability, within the canopy is more robust than the other (which uses a scalar drag coefficient), i.e., it is less sensitive to the inevitable imperfections or approximations in the input data.