The acoustic scattering technique is a powerful tool in the non-destructive control and evaluation of structures. In many real applications, it is important to study the acoustic scattering in bistatic configuration (the emitter is far from the receiver) since it allows to give multiple viewpoints of the considered structure. The present paper investigates both theoretically and experimentally the acoustic scattering in different viewpoints of a cylindrical shell. To analyse the bistatic evolution of the acoustic scattering, we call upon the clockwise and counterclockwise waves propagating on the cylindrical shell. The use of time–angle representation gives a map of the different waves circumnavigating around the shell. This representation allows to show the chronological evolution of the acoustic scattering as a function of the azimuthal angle. The conducted spectral analysis reveals that the frequency content of the scattered acoustic response varies from one location to another. The majority of the resonant frequencies can be detected in the monostatic configuration (the emitter and receiver are co-located). The application of the time–frequency method on the experimental acoustic signals recorded in different viewpoints of the shell allows to analyse and follow the time and frequency shifts of the clockwise and counterclockwise waves propagating on the cylindrical structure. The echo patterns observed in the time–frequency plane are used to estimate the arrival times of the clockwise and counterclockwise waves as a function of the azimuthal angle. Based on the obtained arrival times, we estimate the delay between the clockwise and counterclockwise waves and therefore their group velocities.