Since the penetration depth of neutrons is deep enough to pass through a thick pipe wall, residual stress distributions of inner part of structural materials can be measured by neutron diffraction method. The residual stresses are evaluated three directional strains through Hooke's law. However, the elastic constants depend on the diffraction planes. Thus the neutron diffraction elastic constants of several kinds of materials were measured, and the simplified evaluation method of the diffraction plane dependency of the elastic constants was established. The established method has been applied to the residual stresses in several structural components, especially in the strongly textured materials. Based on those results, the standard for the residual stress measurement by the neutron diffraction was proposed.