A model has been developed for propagation of low-frequency pressure waves in viscoelastic tubes with distensibility of greater importance than compressibility of the liquid. The dispersion and attenuation are shown to be strongly dependent on the viscoelastic properties of the tube wall. The complex, frequency-dependent moduli of relevant tube materials have been measured in a series of experiments using three different experimental procedures, and the data obtained are compared. The three procedures were: (1) ultrasonic wave propagation, (2) transversal resonance in bar samples, and (3) moduli determined by stress wave transfer function measurements in simple extension experiments. The moduli are used in the model to produce realistic dispersion relations and frequency dependent attenuation. Signal transfer functions between positions in the liquid-filled tube can be synthesized from the model and are compared with results of experimental pressure wave propagation in the liquid-filled, flexible tube. A good agreement between experimental data and theoretical predictions is found.