This paper presents a 3D transient numerical approach for thermal and strain/stress modeling of the multilayer laser solid freeform fabrication process, by which correlations between the main process parameters and their effects on the final build-up properties can be studied. This model can be used to optimize the process parameters to increase the controllability of the geometrical and metallurgical variations resulted from the thermal and stress fields. Using this modeling approach, the geometry of the material deposited as well as temperature and thermal stress distributions across the process domain can be predicted based on the process parameters such as powder feed rate, process speed and laser power, assuming the interaction between the laser beam and powder stream is decoupled. The main process parameters affected by a multilayer deposition due to the formation of non-planar surfaces such as powder catchment are also incorporated into the modeling approach. To verify the proposed method, fabrication of a four-layer thin wall of stainless steel AISI 304L on a low carbon steel substrate is modeled with the same process parameters throughout the build-up process. The results show that the temperature and stress slightly increase at the end-points of layers 2, 3, and 4 which cause over deposited materials and micro-crack formations at these regions. The results are then used to discuss optimum process parameters which can be used to have a buildup with better geometrical and physical qualities. The reliability and accuracy of the model are experimentally verified.