The main physiological function of coughing is to remove from the airways the mucus and foreign particles that enter the lungs with respirable air. However, in patients with endotracheal tubes, further surgery has to be performed to improve cough effectiveness. Thus, it is necessary to analyze how this process is carried out in healthy tracheas to suggest ways to improve its efficacy in operated patients. A finite element model of a human trachea is developed and used to analyze the deformability of the tracheal walls under coughing. The geometry of the trachea is obtained from CT of a 70-year-old male patient. A fluid structure interaction approach is used to analyze the deformation of the wall when the fluid (in this case, air) flows inside the trachea. A structured hexahedral-based grid for the tracheal walls and an unstructured tetrahedral-based mesh with coincident nodes for the fluid are used to perform the simulations with the finite element-based commercial software code (ADINA R&D Inc.). Tracheal wall is modeled as an anisotropic fiber reinforced hyperelastic solid material in which the different orientation of the fibers is introduced. The implantation of an endotracheal prosthesis is simulated. Boundary conditions for breathing and coughing are applied at the inlet and at the outlet surfaces of the fluid mesh. The collapsibility of a human trachea under breathing and coughing is shown in terms of flow patterns and wall stresses. The ability of the model to reproduce the normal breathing and coughing is proved by comparing the deformed shape of the trachea with experimental results. Moreover the implantation of an endotracheal prosthesis would be related with a decrease of coughing efficiency, as clinically seen.