Performance of array sonars towed underwater is limited due to the self-noise induced mainly by the strumming vibration of the towing cable and also turbulent flow around the acoustic sensor module. The vibration of the towing cable generates axisymmetric waves that propagate along the acoustic module of the array sonar and produce self-noise. The present study aims to investigate the characteristics of the self-noise induced by the axisymmetric vibrations of the acoustic module. The waves of interest are the bulge and extensional waves propagating along the fluid-filled elastic hose. Dispersion relations of these waves are predicted by means of the numerical simulation to evaluate the wave speeds. The self-noise induced by the axisymmetric waves are formulated taking into account the damping of the elastic hose and the effect of the damping is investigated.