Patient-specific respiratory motion modeling may help to understand pathophysiology and predict therapy planning. The respiratory motion modifies the shape and position of internal organs. This may degrade the quality of such medical acts as radiotherapy or laparoscopy. Predicting the breathing movement is complex, and it is considered as one of the most challenging areas of medical research. This paper presents a biomechanical model of the respiratory system, based on the finite element method (FEM), including the biomechanical behavior of the diaphragm as well as rib kinematics computations, on the assumption that breathing is controlled by two independent actors: the thorax and diaphragm muscles. In order to predict the type of the (geometrical or material) nonlinearities, a quantitative comparison of the clinical data was applied on 12 patients. We propose two nonlinear hyperelastic models: the Saint-Venant Kirchhoff and Mooney–Rivlin models. Our results demonstrate that the nonlinear hyperelastic Mooney–Rivlin model of the diaphragm behaves similarly to the linear elastic model with large displacement (Saint-Venant Kirchhoff). The results suggest that the approach of small strains (within the large displacement) may be globally maintained in the modeling of the diaphragm, and demonstrate that the accuracy of the proposed FEM is capable to predict the respiratory motion with an average surface error in a diaphragm/lungs region of interest contact of 2. 0 ± 2. 3 mm for the contact surface between lungs and diaphragm. The comparison study between the FEM simulations and the CT scan images demonstrates the effectiveness of our physics-based model.