This research focuses on investigating the vibration characteristics of branched circular cylindrical shells with applications to airway passages. Analytical modelling is carried out based on Donnell-Mushtari equations of thin elastic membrane type of shells while numerical validation is conducted using the Finite Element Method (COSMOS/Works). Further validation of the results is performed using experimental investigation of tracheobronchial tissues dissected from pigs. The analytical, numerical and experimental results are in acceptable agreement. Further investigation of the vibration characteristics of the airways for cases which cannot be dealt with analytically is carried out using COSMOS/Works. Results show a strong trend relationship which suggests that the natural frequency of the trachea and the primary tracheobronchi is approximately 10 Hz. Radial resonances of lower bronchi are predictable through trends found in this work that the resonant frequency is a linear function in certain region of generations.