The development of residual stress in metal material additive manufacturing brings a significant obstacle to achieving parts with good quality. The residual stress can be destructive as the structural integrity and mechanical properties are seriously influenced during the manufacturing process. In this work, a finite element method based thermomechanical model is created to simulate the process of direct energy deposition for a copper alloy, GRCop-42. The thermal history of the deposition process is captured, and the development of residual stress & strain is calculated. The result of residual strain development inside the part is compared with the experimental measurement by energy dispersive x-ray diffraction. From the comparison, the result from thermomechanical model shows a high level of consistency with the EDD measurement result in the middle section of the part. However, the EDD result shows a higher residual strain at the left end of the specimen. Non-uniform geometry of printed specimen due to the bulging corners is measured and proved to be the reason for the discrepancy between simulation result and experimental result. Different laser parameters and material properties were also tested in the thermomechanical model to study their influence on the residual stress in additive manufacturing process. The work of this paper provides an approach to understand the development of residual stress, which will be crucial in enhancing the performance of metal additive manufacturing in a wide range of industrial applications.