Patent ductus arteriosus (PDA) presents severe complications such as pulmonary hypertension, left-to-right shunt and cardiac insufficiency. PDA hemodynamics are complex and time-evolving. The purpose of this study is to develop a model of the PDA to improve the understanding of the hemodynamics of the PDA. Methods: A mathematical model was developed with rigid walls, viscous fluid and laminar, pulsatile flow. The control volume includes the aorta, PDA and main pulmonary artery. The boundary conditions used were set at the flow inlets. Flow and pressure conditions in the boundaries are then obtained. A computational model of the PDA was also implemented based on Finite Element Analysis and Computational Fluid Dynamics. This model uses a simple geometry of straight, rigid tubes in the control volume nad boundary conditions described before. This model allows the visualization of the pressure and flow fields in the control volume. Results: The mathematical model mimics the increase in pressure and the volume overflow in the pulmonary circulation (PC). It also shows how the continuing increase in the rigidity of the vessels, in the later stage of the disease affects the flow pattern and produces even a higher pressure in the PC. The 2D computational model also recreates the increase in pressure in the PC, shows the velocity profile and approximates the values of the velocities in every section of the control volume. A significant decrease in velocity and energy loss of the high pressure flow through the PDA when entering the PC is observed. The models are being currently validated with clinical cases.