Computer assisted medical interventions of the heart, liver, digestive or urinary systemhave underlined the need for a reliable, non-invasive three-dimensional technique toassess the respiratory movements, and more particularly the diaphragm displacements.In this context, we present a 3D functional model of the diaphragm based on a discrete biomechanical model. In this model, soft tissues are considered as three-dimensionalelastic component. Elasticity is modeled by minimizing a deformation energy expressedusing a local coordinate system. Muscles are elastic components where the explicitcontraction directions are defined as well as an activation function that generatecontraction forces. Elastic component can be volume constrained to ensureincompressibility.A dynamic MRI study, where the subject respiratory volumes were strictly controlledusing a ventilator, was used to extract the diaphragm shapes and deformations in relationwith the corresponding lung volumes. A 3D diaphragm model was built according toanatomical references and simulation of a respiratory cycle were performed faster thanreal-time. The resulting simulations were confronted with the acquired data. Wecompared the diaphragm deformation and movements as well as the ventilationvolumes. The simulations were accurately simulating the diaphragm piston-like motionand lung volumes variations, although variations is some directions were not correct.