In this paper, we report on residual stress analysis in physical vapour deposited (PVD) CrN coatings. Two 9 µm thick coatings were grown on tool steel substrates with bias voltages of - 50 V and -300 V, respectively. High-energy (E=80 keV) synchrotron radiation measurements have been performed to investigate residual stresses in both as-deposited and annealed CrN coatings. To understand the origins of non-linear distribution of lattice strain versus sin2ψ for certain (hkl) planes in both coatings, a stress orientation distribution function (SODF) analysis has been carried out, which yields grain-orientation-dependent residual stresses. The results are compared to previous analyses using Reuss and Vook-Witt models on the as-deposited coatings.