Acoustic resonance scattering by an air-filled cylindrical shell immersed in water is studied. Complex wave numbers are introduced in order to consider the effects of material (shell) attenuation. Attenuation coefficients are treated as a linear function of incident wave frequency. Scattering form function is numerically calculated and resonance characteristics are analyzed. Firstly, in case where shell attenuation is neglected, resonance width $(\Gamma_{gamma})$ versus resonance frequency $(k_1a)$ is calculated up to $k_1a$=230, or fd=6 (MHz mm) for five ($S_0$, $A_1$, $S_1$, $S_2$, and $A_2$) circumferential wave modes not only for selecting appropriate circumferential wave modes and frequencies, but also for determining frequency regions in which shell attenuation effects should be intensively investigated. Obtained were resonance frequency regions which have relatively narrow resonance width $(\Gamma_{gamma} \le 0.5)$ caused by radiation attenuation. Secondly, the effects of material attenuation on acoustic resonance scattering are investigated in the frequency regions determined in the above for three modes, namely $S_0$, $A_1$, and $S_1$. From these results, ultrasonic attenuation brought the increase of resonance width and the decrease of resonance amplitude. However, the change of resonance frequency is negligibly small. In addition, the component $(\Gamma_{alpha})$of resonance width due to shell attenuation for each mode is linearly increased with k1a and ultrasonic attenuation coefficients. Resonances can be represented by a simple function which is defined by resonance center frequency, peak amplitude, and resonance width. The square of the function representing resonance form is Lorentzian type. The relationships between the change of resonance width and that of peak amplitude due to shell attenuation is as follows. The value of total resonance width times peak amplitude when shell attenuation is taken into account equals to that of resonance width times peak amplitude when shell attenuation is neglected $(\Gamma_{\ast}p_{\ast} = \Gamma_{gamma}p_{gamma})$. Therefore, the variations in peak amplitude is determined by the ratio of the two components of resonance width. Hence, sharp resonances with attenuation neglected are damped out $(p_{\ast} \simeq 0)$when material attenuation is taken into account, because the resonance width caused by material attenuation is far greater than that caused by radiation damping $(\Gamma_{alpha} \gg \Gamma_{gamma})$. Thirdly, experiment was carried out on acoustic resonance scattering from zircaloy-4 cylindrical tube which is used as a nuclear cladding one to isolate and identify $S_0$, and $A_1$ circumferential wave modes. Resonance frequencies are in good agreement with those predicted by numerical analysis. In the case of $S_0$ circumferential wave, some resonances at n=5 and n=6 were not detected. The reason is because ultrasonic attenuation makes those resonances damped out and this is well agreed to the results of numerical analysis. Resonance signal obtained by experiment can be well fitted using the simple function (namely, $\mid{g^{\ast}_n(X)}\mid$) defined by resonance peak amplitude, center frequency, and resonance width.
