The relaxation of strain and stress around the hole during the incremental drilling is studied for a pearlitic steel experimentally and using FEM code ABAQUS. The near surface region was loaded by an equi-biaxial plane stress state, which is typical for the residual stress state caused by quenching in the centre of a rectangular plate. Strain relaxation at the strain gage positions during the incremental drilling of the hole is calculated and compared to experimental results, determined both by strain gage readings and X-ray diffraction. It is shown that local plastic deformations lead to a higher elastic strain relief at the surface compared to the purely elastic state. As a consequence overestimated residual stress values are calculated by the hole drilling evaluation methods. Comparing the results of elastic and elasto-plastic FE-analyses and by an additional variation of the initial residual stress magnitude, errors for the strain relaxation and for the determined residual stress components are given as a function of the initial residual stress related to the material's yield strength and the hole depth. These errors characterise the quantity of overestimation of the residual stresses determined by the hole drilling method if plastic deformations are present in the vicinity of the hole.