Both　the　formation　energies　and　the　intra-　and　inter-layer　activation　energies　of　self-diffusion　of　a　single　vacancy　in　the　first　six　planes　of　Pd(001)　surface　have　been　investigated　by　means　of　molecular　dynamics　(MD)　in　conjunction　with　the　semi-experiential　many-body　potential　of　the　modified　analytical　embedded-atom　method　(MAEAM).　The　results　show　that　the　effect　of　the　surface　on　the　vacancy　is　only　down　to　the　fifth-layer.　It　is　easer　for　a　single　vacancy　to　form　and　to　migrate　in　the　first　layer.　Furthermore,　the　vacancy　in　the　second　layer　is　favorable　to　migrate　to　the　first　layer.　This　is　in　agreement　with　the　experimental　results　that　the　first　layer　has　the　highest　concentration　of　the　vacancy.　(c)　2006　Elsevier　Ltd.　All　rights　reserved.