The wave speed in initially elliptical collapsible tubes was studied. The celerity c of pressure waves of small amplitude was calculated from the numerically defined area-pressure law of the buckled cross section. In addition to the fact that the wave speed variation with transmural pressure was strongly dependent upon the initial eccentricity of the cross section, the wave speed value was found to be discontinuous at the contact pressure pc and reached a minimum on the right-hand side of the discontinuity. These results were compared with experimental data obtained in an annular duct.