Abstract: In the process of laser aided direct metal deposition(DMD), the control of thermal-induced residual stress is very difficult,because the stress is affected by many parameters including geometricaldimensions, material properties and process parameters. In this paper,dimensional analysis is employed to extract key dimensionless parametersof geometry, heat transfer and thermal deformation.In addition, a 3D transient FEA model is proposed to studythe effects of these key dimensionless parameters on the residual stress. Itis shown that the residual stress can be controlled by employing materialswith relatively small thermal expansion coefficient or small yield stress.Furthermore, the residual stress can be reduced by decreasing heat loss,increasing laser power, especially, by increasing preheat temperature.