Although additive manufacturing is fast gaining traction in the industrial world as a reputable manufacturing technique to complement traditional mechanical machining, it still has problems such as porosity and residual stresses in components that give rise to cracking, distortion, and delamination, which are important issues to resolve in structural load-bearing applications. This research project focused on the characterization of the evolution of residual stresses in Ti-6Al-4V extra-low interstitial (ELI) additive-manufactured test samples. Four square thin-walled tubular samples were deposited on the same baseplate, using the direct energy deposition laser printing process, to different build heights. The residual stresses were analysed in the as-printed condition by the neutron diffraction technique and correlated to qualitative predictions obtained using the ANSYS software suite. Good qualitative agreement between the stress measurements and predictions were observed. Both approaches revealed the existence of large tensile stresses along the laser track direction at the sections that were built last, i.e., centre of the top layers of the samples. This in addition leads to large tensile stresses at the outer edges (corners) which would have the effect of separating the samples from the baseplate should the stresses exceed the yield strength of the material. Such extreme conditions did not occur in this study, but the stresses did lead to significant distortion of the baseplate. In general, the microstructures and spatial elemental mapping revealed a strong correlation between the macro-segregation of elemental V and the distribution of the β-phase in the printed parts.