A significant problem associated with additively manufactured components is the development of high residual stresses. These residual stresses, in turn, trigger distortions/warping when removing the part from the build substrate or increase the probability of crack initiation, both during the building process and in-service loading. Understanding residual stress evolution in printed samples is crucial for manufacturers to optimize the component design and mitigate the adverse effects of residual stresses. Ti6Al4V has a diverse range of applications, extending from the production of very thin struts to large aerospace components. The component geometry significantly influences the distribution of residual stresses. Thus, it is important to understand the effect of geometry on the residual stress evolution of LPBF-built Ti6Al4V components. Three-dimensional finite element models are used to simulate the LPBF process to estimate the thermal and residual stress profiles. Thin walls of different thicknesses and build heights have been investigated to comprehend the impact of build geometry. Overall, this research work provides a deeper understanding of the relationship between geometrical aspects and residual stress development in Ti6Al4V components, which aids in optimizing the AM process and post-build heat treatments according to the specific requirements.