Over the last twenty years, many ideas have been suggested to design sub-wavelength absorbers that couple a classical single-degree of freedom liner with a vibrating part that resonates at low frequencies. In this paper, the acoustic behaviour of a light and thin sound absorber composed of an elastic latex membrane placed on top of a closed 3D-printed cavity is studied. It is found experimentally and analytically that membrane modes imply a great shift of the cavity resonance towards the low frequencies and add several supplementary transmission drops. To investigate the effects of flow, numerical time-domain simulations are conducted and validated after comparisons with experimental data. The three approaches show that membrane absorbers are highly resistive, with a weak sensibility against flow and non linear effects. They are thus well-suited for absorption purposes in aeronautic applications.