The spatial, linear stability of an incompressible parallel boundary layer flow with uniform suction through the wall is studied for the case of rigid and flexible bounding surfaces. It is demonstrated, first, that the effect of the plate’s permeability is crucial in defining the disturbance boundary conditions at the wall, and that stability limits depend strongly on it. Next, the combined effect of plate’s permeability and compliance on the onset of Tollmien Schlichting modes is assessed. Finally, the possible insurgence of an absolute instability mode is studied, as function of the Reynolds number, the modulus of elasticity of the plate, and its permeability.