Trachea and the bronchi are responsible for air transport in the respiratory system during inhalation and exhalation. The paper aims to numerically analyze the airflow in a 3D reconstructed model of a patient-specific trachea and bronchi based on computed tomography images. The critical areas are identified by investigating the main fluid dynamics parameters, such as the velocity field, pressure field and wall shear stress. The paper provides a detailed approach to the phenomena occurring in the bifurcation regions of the trachea and the main bronchi. The results may contribute to the improvement of therapeutic techniques related to the respiratory system, with possible applicability in enhancing aerosol distribution and mechanical ventilation methods. Thus, this study offers a better understanding of the aerodynamic processes in the trachea, with potential impact on the development of more efficient medical solutions for lower respiratory tract conditions.