Transcatheter aortic valve replacement (TAVR) has emerged as an effective alternative to conventional surgical valve replacement in high-risk patients afflicted by severe aortic stenosis. Despite newer-generation devices enhancements, post-procedural complications such as paravalvular leakage (PVL) and related thromboembolic events have been hindering TAVR expansion into lower-risk patients. Computational methods can be used to build and simulate patient-specific deployment of transcatheter aortic valves (TAVs) and help predict the occurrence and degree of PVL. In this study finite element analysis and computational fluid dynamics were used to investigate the influence of procedural parameters on post-deployment hemodynamics on three retrospective clinical cases affected by PVL. Specifically, TAV implantation depth and balloon inflation volume effects on stent anchorage, degree of paravalvular regurgitation and thrombogenic potential were analyzed for cases in which Edwards SAPIEN and Medtronic CoreValve were employed. CFD results were in good agreement with corresponding echocardiography data measured in patients in terms of the PVL jets locations and overall PVL degree. Furthermore, parametric analyses demonstrated that positioning and balloon over-expansion may have a direct impact on the post-deployment TAVR performance, achieving as high as 47% in PVL volume reduction. While the model predicted very well clinical data, further validation on a larger cohort of patients is needed to verify the level of the model’s predictions in various patient-specific conditions. This study demonstrated that rigorous and realistic patient-specific numerical models could potentially serve as a valuable tool to assist physicians in pre-operative TAVR planning and TAV selection to ultimately reduce the risk of clinical complications.