Additive manufacturing technologies have numerous advantages over conventional technologies; nevertheless, their production process can lead to high residual stresses and distortions in the produced parts. The use of numerical simulation models is presented as a solution to predict the deformations and residual stresses resulting from the printing process. This study aimed to predict the tensions and distortions imposed in the gear repair process by directed energy deposition (DED). First, the case study proposed by National Institute of Standards and Technology (NIST) was analyzed to validate the model and the numerically obtained results. Subsequently, a parametric study of the influence of some of the parameters of DED technology was carried out. The results obtained for the validation of the NIST benchmark bridge model were in agreement with the results obtained experimentally. In turn, the results obtained from the parametric study were almost always in line with what is theoretically expected; however, some results were not very clear and consistent. The results obtained help to clarify the influence of certain printing parameters. The proposed model allowed accounting for the effect of residual stresses in calculating the stresses resulting from gear loading, which are essential data for fatigue analysis. Modeling and simulating a deposition process can be challenging due to several factors, including calibrating the model, managing the computational cost, accounting for boundary conditions, and accurately representing material properties. This paper aimed to carefully address these parameters in two case studies, towards reliable simulations.