To understand how the input impedance of the respiratory system relates to pressure and volume airflow of the airway branched structure, this thesis focuses on developing a mathematical model of the branched airway including trachea and branching airways. The 5-Lobe lung model is developed mathematically and experimentally. A computer model is constructed in the MathlabTM programming environment. It accounts for the effects of airways with varying cross-sectional area, flexible wall properties, and the bronchial tree within the lung using the mathematical methods developed in previous researches. The terminal impedances are determined by proposed idealized lobe models. A range of frequencies up to 256 Hz are tested on this model. Cases of study on obstructions by varying lung stiffness from healthy to unhealthy conditions are investigated.Mathematical model is validated by experiment investigations on the mechanical lung simulator, which is built in Diagnostic & Control Research Centre at Auckland University of Technology. The results conclude that mathematical methods used in this research are capable to produce predictable results of the input impedance.