The hole drilling method is a widely known technique for the determination of non-uniform residual stresses in metallic structures by measuring strain relaxations at the material surface caused through the stress redistribution during drilling of the hole. The integral method is a popular procedure for solving the inverse problem of determining the residual stresses from the measured surface strain. It assumes that the residual stress can be approximated by step-wise constant values, and the material behaves elastically so that the superposition principle can be applied. Required calibration data are obtained from finite element simulations, assuming linear elastic material behavior. That limits the method to the measurement of residual stresses well below the yield strength. There is a lack of research regarding effects caused by residual stresses approaching the yield strength and high through-thickness stress gradients as well as the correction of the resulting errors. However, such high residual stresses are often introduced in various materials by processes such as laser shock peening, for example, to obtain life extension of safety relevant components. The aim of this work is to investigate the limitations of the hole drilling method related to the effects of plasticity and to develop an applicable and efficient method for stress correction, capable of covering a wide range of stress levels. For this reason, an axisymmetric model was used for simulating the hole drilling process in ABAQUS involving plasticity. Afterward, the integral method was applied to the relaxation strain data for determining the equibiaxial stress field. An artificial neural network has been used for solving the inverse problem of stress profile correction. Finally, AA2024-T3 specimens were laser peened and the measured stress fields were corrected by means of the trained network. To quantify the stress overestimation in the hole drilling measurement, an error evaluation has been conducted.