Over the last years, the aging population and people more active in sports have been correlated to an increasing demand of prostheses and biomedical implants, most of which are made of Ti6Al4V alloy, since it assures elevated corrosion resistance, good mechanical properties and biocompatibility. In the hip replacement, the acetabulum in the pelvis is replaced by a Ti6Al4V acetabular cup, which is currently manufactured through Additive Manufacturing (AM) technologies and machining operations. Nevertheless, this process presents some critical drawbacks in the production of acetabular cups characterized by a high surface-to-thickness ratio, such as the elevated distortions in AM and the significant waste of material in machining operations to reach the final shape. Therefore, the alternative idea suggested and investigated in this PhD project is the application of sheet forming processes to be carried out at elevated temperature to increase the limited formability that Ti6Al4V shows at room temperature. Aiming at identifying the proper working conditions, the research work focused on three main topics, namely (i) the investigation of the material behaviour and biomedical properties to address the forming issue and assure a good osseointegration process at the implant-bone interface, respectively; (ii) the modelling of material rheology and ductility; (iii) the manufacturing of a prototype. Following this approach, because a review of literature showed that Ti6Al4V has been mostly investigated at low strain rates typical of the superplastic regime, the material behaviour was first explored in a wide range of temperatures and moderate strain rates, pointing out the relations between the mechanical and microstructural properties. Based on these results, the process conditions necessary to address the forming issue were identified, since higher temperatures higher ductility. However, the preservation of the material bioactivity, which was enhanced through the application of different surface treatments, was found to limit the forming temperature to a maximum value. The research work on the material modelling raised from the increasing interest of the industrial and scientific communities on the use of Finite-Element (FE) models to numerically assess the manufacturing process. In this context, the Ti6Al4V flow stress behaviour was modelled applying the well-known Johnson-Cook and Arrhenius-type constitutive models, while great efforts were addressed to propose a new model able to describe the ductility of Ti6Al4V sheet in a wide range of temperatures and stress states. With this aim, the original Johnson-Cook fracture strain criterion was modified to incorporate a quadratic function of the stress triaxiality and Lode parameter, whose coupled effect was recently recognized to have a significant role in predicting the fracture occurrence also in more complex stress states. On the other hand, a quadratic function of the temperature was introduced to represent the transformation related ductility inherent in the two phase (α/β phases) titanium alloy Ti6Al4V at elevated temperatures. Finally, Incremental Sheet Forming (ISF) process was chosen to manufacture the biomedical part because, according to literature, ISF technique is suitable for small volume batches and high customized sheet metal parts, as the case of biomedical implants. Different variants of ISF process were electrically-assisted to manufacture difficult-to-form Ti6Al4V sheets, and their results were evaluated in terms of final shape and surface characteristics, the latter playing a key role in the biological phenomena at the basis of the osseointegration process. In addition, within the same manufacturing topic, a variant of ISF process was selected to investigate the fracture phenomenon and provide a deeper understanding of the relations between the process mechanics and the fracture occurrence.