During Atrial Fibrillation (AF) more than 90% of the left atrial thrombi responsible for thromboembolic events originate in the left atrial appendage (LAA), a complex small sac protruding from the left atrium (LA). Current available treatments to prevent thromboembolic events are oral anticoagulation, surgical LAA exclusion, or percutaneous LAA occlusion. However, the mechanism behind thrombus formation in the LAA is poorly understood. The aim of this work is to analyse the hemodynamic behaviour in four typical LAA morphologies - “Chicken wing”, “Cactus”, “Windsock” and “Cauliflower” - to identify potential relationships between the different shapes and the risk of thrombotic events. Computerised tomography (CT) images from four patients with no LA pathology were segmented to derive the 3D anatomical shape of LAA and LA. Computational Fluid Dynamic (CFD) analyses based on the patient-specific anatomies were carried out imposing both healthy and AF flow conditions. Velocity and shear strain rate (SSR) were analysed for all cases. Residence time in the different LAA regions was estimated with a virtual contrast agent washing out. CFD results indicate that both velocity and SSR decrease along the LAA, from the ostium to the tip, at each instant in the cardiac cycle, thus making the LAA tip more prone to fluid stagnation, and therefore to thrombus formation. Velocity and SSR also decrease from normal to AF conditions. After four cardiac cycles, the lowest washout of contrast agent was observed for the Cauliflower morphology (3.27% of residual contrast in AF), and the highest for the Windsock (0.56% of residual contrast in AF). This suggests that the former is expected to be associated with a higher risk of thrombosis, in agreement with clinical reports in the literature. The presented computational models highlight the major role played by the LAA morphology on the hemodynamics, both in normal and AF conditions, revealing the potential support that numerical analyses can provide in the stratification of patients under risk of thrombus formation, towards personalised patient care.