The conventional Sachs method and a new method using Fourier analysis are employed to measure non-axisymmetric residual stresses. Two examples of non-axisymmetric residual stresses are presented. The first is a highly non-axisymmetric residual stress distribution around a plain hole exposed to creep conditions. The second example deals with residual stresses arising in a cold expanded hole. The two residual stress measurement techniques rely on strain measurements in hoop and/or axial directions at a given radial distance. The Sachs method assumes that the residual stresses are symmetric, and consequently only one strain gauge is needed. However, for the new method the strain distribution at several angles is required. The angular strain measured, as a result of boring out the hole, for both examples were found to exhibit significant variations. The calculated residual stresses from both techniques are discussed and compared. The error introduced using Sachs method depends on the angular variation of the residual stresses. Not only can the conventional Sachs technique give erroneous residual stress magnitudes, but can also provide residual stresses of the opposite sign. The new method is shown to provide accurate results.