Atrial fibrillation is a disease that alters the speed and rhythm of the heartbeat, greatly affecting the patient’s quality of life. To treat recurrent forms, the pulmonary veins are electrically isolated, freezing the cardiac tissue surrounding them. This treatment is carried out using a cardiac probe consisting of a capillary for the delivery of the coolant in a balloon expansion chamber, and a return line to discharge the exhausted fluid. The aim of this thesis is to develop a 1-D numerical model of a balloon-based cryogenic probe to analyse the phenomena involved. The behaviour of the fluid inside the injection and return line was modelled using the continuity, momentum and energy equations written under the assumption of steady-state implementing an homogeneous model for two-phase fluid.