The contour method relies on deformations that occur when a residually stressed component is cut along a plane. The method is based on the elastic superposition principle. When plasticity is involved in the relaxation process, stress error in the resulting measurement of residual stress would be caused. During the cutting the specimen is constrained at a location along the cut so that deformations are restrained as much as possible during cutting. With proper selection of the constraining location the plasticity effect can also be minimized. Typical patterns of longitudinal welding residual stress state were taken to assess the plasticity effect along with constraining locations.