Technical components produced via sheet metal forming often obtain characteristic crystallographic textures and process induced residual stress distributions. Knowledge of the local residual stress states is essential for the proper components' dimensioning. We report about the expansion of the incremental hole drilling technique for residual stress analysis to highly textured material states. A new evaluation approach using the differential evaluation algorithm is proposed, which bases on the calculation of multiple case specific calibration functions under consideration of the local orientation distribution function of the textured material. Systematic finite element (FE) simulations of incremental hole-drilling experiments are conducted regarding defined ideal nickel single crystal orientations (cube, Goss and brass). Multiple casespecific calibration functions, which consider the materials elastic anisotropy, are calculated and applied for stress calculation. In addition, the influence of a rosette misorientation between stress measurement and FE calibration is investigated. Using this new evaluation strategy a significant improvement of (residual) stress calculation on strongly textured materials is achieved. Finally, the capability of the proposed evaluation approach is experimentally validated for an uniaxially loaded CMSX-4 (nickel base super alloy) single crystal. The investigation clearly proved that in case of strongly anisotropic materials the evaluation using multiple case-specific calibration functions leads to a significant improvement in stress analysis compared to a conventional evaluation.