It is compelling to realize that the additive manufactured part using wire feeding type directed energy deposition (DED) process is subjected to undesired thermal effects, and induced residual stress during the manufacturing process. In order to improve the quality of the manufactured part, the distributions of temperature and residual stress have to be understood to manage the results of the processing of these materials. The objective of this paper is to investigate the influence of the angle of corner deposition on the distributions of temperature and residual stress of the Ti-6Al-4V deposited bead, and the substrate via thermo-mechanical finite element analyses (FEAs). In the same fashion, the formation of the heat affected zone (HAZ) and the stress influenced region (SIR) are estimated from the measured results of the FEAs. Equally important, it can be stated that from the estimated HAZ and SIR regions, the overlapping of undesired thermal effects and residual stress between two beads fabricated by the wire feeding type DED process can be avoided at the design stage.