Abstract When the hole-drilling method is used to measure residual stress, plasticity effects occur if the residual stress exceeds 60 % of the yield stress. Plasticity effects result in an overestimation of the residual stress as the hole-drilling method is based on the linear elastic behavior of materials. To overcome this problem, a simplified iterative method based on an existing iterative method and using the optimizer tools of the ANSYS program is proposed in this paper. The proposed method is verified through numerical and experimental studies. The numerical case study reveals that, for the case studied, the proposed method can achieve the same accuracy as the original iterative method and has a higher convergence ability. The experimental study demonstrates that the values of the maximum principal stress calculated using the American Society of Testing Materials standard is generally greater than the true values and that the error magnitude increases with an increase in stress levels. Using the proposed method, errors are reduced for the maximum principal stress while increasing slightly for the minimum principal stress. The proposed method has a high convergence ability; for the case studied, only two or three iterations are needed to achieve acceptable accuracy.