Transcatheter aortic valve implantation (TAVI) enables treatment of aortic stenosis with no need for open heart surgery. According to current guidelines, only patients considered at high surgical risk can be treated with TAVI. In this study, patient-specific analyses were performed to explore the feasibility of TAVI in morphologies, which are currently borderline cases for a percutaneous approach. Five patients were recruited: four patients with failed bioprosthetic aortic valves (stenosis) and one patient with an incompetent, native aortic valve. Three-dimensional models of the implantation sites were reconstructed from computed tomography images. Within these realistic geometries, TAVI with an Edwards Sapien stent was simulated using finite element (FE) modelling. Engineering and clinical outcomes were assessed. In all patients, FE analysis proved that TAVI was morphologically feasible. After the implantation, stress distribution showed no risks of immediate device failure and geometric orifice areas increased with low risk of obstruction of the coronary arteries. Maximum principal stresses in the arterial walls were higher in the model with native outflow tract. FE analyses can both refine patient selection and characterise device mechanical performance in TAVI, overall impacting on procedural safety in the early introduction of percutaneous heart valve devices in new patient populations.