An inverse method is developed for measuring the breathing wave speed in a liquid-filled cylindrical shell. The model used with this method is based on an experimental configuration in which a long cylindrical shell is longitudinally excited by a mechanical shaker at one end. The resulting longitudinal wave propagation produces a spatial field in the shell that consists of extensional and breathing waves. End-mounted accelerometers and force transducers are used to measure the extensional wave speed. Once this is accomplished, transfer functions between five equally spaced hydrophones (in the fluid) and a forward accelerometer are recorded. These data are then combined to yield a closed-form value of the complex, frequency-dependent breathing wave speed. The experiment included to validate this method is extremely easy to implement and can be rapidly executed.