The Sachs boring technique is used widely to determine residual stresses in axisymmetric components. Several studies have attempted to use this standard method to determine residual stresses where the measured strains are non-axisymmetric. In this paper a new procedure to measure non-axisymmetric residual stresses is presented. The new method is based on a Fourier analyses of the measured strains. The analysis determines radial, tangential and shear tangential stresses as a function of angle and radial distance. The solutions provided can be applied to plane stress and plane strain conditions. The accuracy of the new method is validated using a FE simulation to generate a non-axisymmetric residual stress distribution. FE simulation of material removal and strain readings is also conducted. Finally the residual stresses are calculated using both Sachs conventional axisymmetric analysis and the new Fourier analysis. The new method determines accurately the non-axisymmetric residual stress distributions, while the conventional method provides only an average distribution.