Residual Stresses (RS) in mechanical components can be undesirable, and their accurate identification can prevent component damage. There are many semi-destructive methods for determination of RS. The hole-drilling method offers many advantages when compared to other methods due to its practicality, applicability to different materials, and low-cost execution. According to the American Society for Testing and Materials (ASTM) E837- -13a Standard, the RS are assumed to be constant at each depth level when employing the hole-drilling method. Thus, calibration coefficients are necessary to calculate stress values at each level using the relaxed strains measured on the component surface, as incremental drillings are performed. However, the coefficients provided by the Standard were obtained using a coarsely-discretized 2D finite element model. This work aims to find new calibration coefficients based on the linear elasticity theory and using the Finite Element Method (FEM) with a refined mesh. A numerical model consisting of linear tetrahedral finite elements was constructed to simulate the resulting strains, as unitary stresses are applied at each depth level of the component inner surface. Using this method, two matrices of calibration coefficients are obtained, one related to normal stresses, and another related to shear stresses. The results show that the RS obtained using the new coefficients presented a 3.9% relative average error compared to analytical values in the four experiments conducted, while the ASTM Standard coefficients resulted in a 9.7% relative average error.