The scattering of elliptical cylinders of infinite length insonified by an incident beam perpendicular to their axis is investigated. The method of isolation and identification of resonances (MIIR) allows one to plot resonance spectra. These spectra are obtained from three targets characterized by their major radius/minor radius ratio equal to 4/3, 4/2, 4/1. The resonance spectra obtained from a circular cylinder excited in the same conditions show peaks related to circumferential waves which, for particular frequencies, constitute standing waves. In this case, the phase velocity depends only on the frequency. Contrary to the circular cylinder, resonance spectra obtained by an experimental monostatic method depend on the azimuthal position of the transducer. Some resonances vanish at certain positions. In this case, the phase velocity and the coupling coefficient are a function of the curvature radius and the frequency. The wavelength is not identical on the circumference of the elliptical cylinder. To explain the experimental results, a phase-matching model is developed to determine the resonance frequencies [H. Uberall et al., J. Acoust. Soc. Am. 81, 312--315 (1987)]. This method allows one to represent the vibration state on the circumference. An integral calculus applied on the latter result gives the far-field pressure.