The propagation of ion‐acoustic waves in a weakly ionized, bounded plasma is investigated, typically with reference to discharge tubes, where a flow of plasma towards the walls is required to ensure the balance between volume ionization and surface recombination. A macroscopic description is used which accounts for effects of ion‐neutral collisions and finite ion temperature. Special attention is paid to the problem of the wave absorption at the plasma boundary. It results that the ion‐acoustic waves are strongly absorbed at the plasma boundary whenever the electrostatic boundary conditions require the formation of a space‐charge sheath near the walls (implying the existence of a transonic point of the plasma flow at the limit between the sheath and the plasma). The situation where no transonic point exists is also discussed.