The change in strain is monitored by on-line computer as a function of cut depth. The principal residual stresses are determined using the derivative of the strain data as a function of depth. The ring-core technique can be used on metals. ceramics, and polymers, where linear elastic theory can be assumed. The techniques is most useful in quantifying the residual stresses in coarse grained weldments, in which diffraction techniques cannot used. The method is practical for large nickel-base forged components because of its efficiency in determining the residual stresses at greater depths.