The　objective　of　this　paper　is　to　understand　the　effect　of　thermally　grown　oxide　(TGO)　on　the　multiple　surface　cracking　behaviors　in　an　air　plasma　sprayed　CAPS)　thermal　barrier　coating　system　(TBCs).　The　extended　finite　element　method　(XFEM)　and　periodic　boundary　conditions　are　used　to　investigate　the　TGO　dependences　of　periodic　surface　crack　driving　force　and　crack　propagation　path.　It　is　seen　that　the　effect　of　TGO　thickness　on　the　strain　energy　release　rate　(SERR)　is　negligible　while　ignoring　the　thickening　and　elongation　strains　of　the　TGO　layer.　However,　the　effect　of　elastic　modulus　of　TGO　layer　is　significant.　In　particular,　for　relatively　stiff　TGO　layer　the　SERR　drops　to　zero　as　the　ratio　of　surface　crack　length　to　coating　thickness　approximates　to　one.　And　vice　versa,　for　a　severely　damaged　TGO　layer　with　relatively　compliant　modulus,　the　SERR　approaches　infinity　as　surface　cracks　propagate　to　the　interface.　This　kind　of　fracture　mechanism　is　mainly　governed　by　the　elastic　mismatch　across　the　bimaterial　interfaces,　which　can　be　used　as　a　guide　for　the　design　of　good　strain-tolerant　coating　film　in　APS-TBCs.　(c)　2012　Elsevier　B.V.　All　rights　reserved.