An analytical approach to the acoustic input impedance of vibrating cylindrical pipes is considered. The variation in the acoustic impedance introduced by wall vibrations is calculated using the integro-modal method taking into account axisymmetric shell vibration. It is shown that this variation can be interpreted as a small correction in the acoustic input impedance when the walls of the shell do not influence the acoustics in the pipe. Special conditions such as the mechanical resonance condition and spatial coincidence effect lead to maximum values of the correction factor for the input impedance. The results allow us to determine particular shell parameters for which the input impedance is strongly affected by wall vibrations.