Mechanical strain relief covers a class of techniques for measuring residual stress in engineering components. These techniques work by measuring strains or displacements when part of the component is machined away. The assumption is that such strain or displacement changes result from elastic unloading; however, in components containing high magnitudes of residual stress elastic–plastic unloading may well occur. Such elastic–plastic unloading introduces errors into the measurement of the residual stresses and these errors may be large. This paper addresses the performance of the deep hole drilling technique, a mechanical strain relief technique particularly suitable for large section components. First a plane strain analysis is presented that quantifies the errors associated with plasticity for different magnitudes of residual stress. A three dimensional finite element analysis is then carried out that shows larger errors may be obtained than those suggested by the plane strain analysis. A method for reducing the magnitude of the error is investigated. Finally, the results of an experimental measurement of residual stress are presented where substantial plasticity occurs. The work demonstrates the potential vulnerability of mechanical strain relief methods to plasticity and introduces methods for quantifying the resulting errors. It also provides further evidence that modifications to the standard DHD technique can be made to make the technique less susceptible to error when plasticity occurs.