Weld residual stress (RS) measurements are often undertaken on test-pieces which have been cut out from large components, yet it remains unclear to what extent the RSs in test-pieces are representative of those present in the original component. Similarly weld mechanical performance tests are frequently undertaken on cross-weld test-pieces without a proper understanding of the level or influence of retained RS. We present a systematic study of the relaxation of longitudinal RS in thin-plate butt welds produced using different materials and welding methods (FSW, laser-MIG, and pulsed-MIG). In each case the RSs were measured repeatedly in the same location as the welds were progressively and symmetrically cut down. Although cutting inevitably leads to stress redistribution, significant relaxation of the longitudinal RS was only observed when the weld length or width was reduced to below a certain value. This critical value appears to correlate with the lateral width of the tensile zone local to the weld-line and may be considered to be the characteristic length as defined in St. Venant’s principle. Further, it was found that the level of stress relaxation as a function of weld length for all the welds studied could be collapsed onto a single empirical curve using a simple approach based on the characteristic length scales of the weld. Given the range of materials and welding methods used, this relation appears to be of general use for thin-plate welds although further work is required to test the limits of its applicability.