Let　the　elastic　domain　be　a　disk,　and　its　boundary　the　unit　circle.　By　dint　of　the　stability　of　Cauchy-type　integral　with　respect　to　the　perturbation　of　integral　curve,　this　paper　discusses　the　stability　of　the　complex　stress　functions　to　the　second　fundamental　problem　in　plane　elasticity　when　smooth　perturbation　happens　for　the　boundary　curve.　Copyright　(C)　2010　John　Wiley　&　Sons,　Ltd.