Residual stress measurement techniques using mechanical strain relaxation depend on a number of physical quantities and are therefore sensitive to errors associated with the measured data. The resulting stress uncertainties can easily become significant and compromise the usefulness of the results or lead to misinterpretation of the behaviour of the residual stress distributions. It is therefore essential to develop an error analysis procedure for the measurements undertaken. Error analysis procedures for the deep hole drilling (DHD) method are developed to consider triaxial residual stresses. A modified deep hole drilling method, called the incremental deep-hole drilling (iDHD), was applied to measure the near yield residual stress distributions in a cold water quenched aluminium 7010 alloy forged block. The experimental results are used to illustrate the errors.