A thermo-mechanical finite element model is developed to determine the temperature history and residual stresses in a Cu-H13 thin-walled plate deposited by the Laser Engineered Net Shaping (LENSTM) process. The same model is also applied to a H13-H13 sample to compare the results. The input laser power is adjusted to maintain a steady molten pool size and depth. For a constant scanning speed the laser power decreases with the addition of more layers, and with the increase of scanning speed the laser power needs to be increased. The Z-component of residual stresses is greater than the other components, and is compressive near the center of the wall and tensile at the free edges. The residual stress levels near the free edges are higher in the H13-H13 sample than in the Cu-H13 sample. In these regions, the use of unidirectional scanning results in a higher stress accumulation than the alternating scanning.