Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive, fibrosing interstitial lung disease of unknown etiology characterized by a poor prognosis and no proven effective treatment. Some pathological conditions such as fibrosis, make the lungs become stiffer due to the development of less flexible connective tissue, but the clinical course of IPF is variable making it difficult to estimate the progress of the disease. Simulating lung behaviour during the respiratory cycle is a difficult task because of its complex geometry and surrounding environmental constraints. Moreover, the lack of information and even more the difference in literature values for mechanical properties increase the level of difficulty. The main goal of this project was to simulate lung expansion during inspiration on a continuum media mechanics model solved with a finite element method (FE). No detailed modeling of lung structures at atomic or molecular scale will be required, the assumption of continuum media will be applied to macroscopic level definition of organs. To obtain accurate representations, specialized for each patient, two lung models were created based on Computed Tomographies. On a first approach, a model of a healthy lung was developed with the purpose of linking aspects of breathing physiology to a corresponding contact problem of elasticity theory which was be solved by the finite element method. Finally on a second stage, a lung corresponding to a patient with IPF was modelled and subjected to the same conditions for comparison. Results show that the best configuration is achieved by setting the properties of the fibrotic tissue as more than six times higher than the properties of the healthy tissue (E healthy= 10 kPa and E fibrotic= 65 kPa). In both models the pressure required to obtain full expansion was 36 kPa, the difference stands on the volume difference to overcome, which was considerably low in the case of the fibrotic lung. The fibrotic tissue is subjected to higher stresses and lower strains, the differences in stress and strain distributions between the healthy and the fibrotic model arise from the fact that the procedure for obtaining the meshes was not the same in both cases. This factor should be taken into account in the future for further improvement of the healthy mode.