X ray computer tomography for the measurement of triaxial stresses within a low atomic order material is presented to aim at the shortcoming of conventional X ray stress analysis and AST2001 X ray stress analyzer of USA. The device for X ray computer tomography of residual stresses and the measurement theory is discussed. The computer procedure for the measurement of X ray computer tomography is designed. With the diffraction data provided, complete triaxial stresses of an arbitrary point on the surface of and within material investigated can be evaluated. The stress tensors, stress gradients and stress free lattice spacing of material investigated can also be calculated. And a self control mechanism for measurement and evaluation is presented.