A theoretical investigation of the effects of structural restraint, repair depth and wall thickness on the distribution of transverse residual stresses at repair welds in heavy-section plates and cylindrical structures has been conducted using a computer program. The applicability of the program was demonstrated by comparison with experimental measurements at a 28-mm-deep repair weld in a 75-mm-thick carbon-manganese steel test panel. The computed stresses were in good agreement with the experimental results, and the analysis showed why the net membrane stress in the panel at the repair weld was compressive. The program was then used to investigate the effects on the residual stress distribution of the different levels of restraint present at repairs of various lengths in flat plates, and at full length axial repairs, full circumferential repairs and part-circumferential repairs in cylinders. It was also used yo investigate the effects of repair depth and wall thickness. In nearly all cases, the stresses were computed to be of yield magnitude in tension at the repaired surface and to decrease with depth from the surface.