In　the　design　of　thin-walled　spot　welding　structures　such　as　the　automobile　body　structure,　it　is　necessary　to　evaluate　the　fatigue　strength　of　spot　welding　at　the　good　accuracy.　The　evaluation　by　using　stress　intensity　factor　K　in　the　linear　elastic　fracture　mechanics　is　carried　out,　because　the　contact　surface　of　the　joint　by　spot　welding　can　be　considered　annular　crack.　In　this　study,　as　the　fundamental　research　of　crack　propagation　analysis　in　the　thin　plate　spot　welding　joints,　double　cup　spot　welding　joint　(DC　joint)　which　was　thin　plate　spot　welding　joint　developed　for　multiaxial　loading　fatigue　specimen　was　analyzed　in　enriched　element-free　Galerkin　method　(Enriched　EFGM),　and　the　accuracy　of　the　solution　of　the　stress　intensity　factor　was　examined.