This work reports on a study to develop a patient-specific finite element model of the Transcatheter Aortic Valve Implantation procedure, using a model of a balloon-expandable percutaneous prosthetic aortic valve as a framework for the prediction of its performance. An experimentally measured left ventricle and aortic pressure profile of a single systolic-diastolic cycle of a resting heart are used to assess the performance of the stent after its deployment. The results of the simulation show that the stent maintains its structural integrity after deployment, and successfully pushes the native leaflets back to keep the aortic root clear of all impediments.