This　paper　develops　the　dual　boundary　element　method　(DBEM)　using　a　new　fundamental　singular　solution.　This　new　solution　is　the　elastic　fields　of　transversely　isotropic　multilayered　materials　of　infinite　extent　under　point　concentrated　loads.　The　discretization　technique　is　utilized　to　approximate　arbitrary　variations　of　functionally　graded　materials　(FGMs)　with　transverse　isotropy　in　a　graded　direction.　The　proposed　DBEM　is　used　to　analyze　the　three-dimensional　crack　problems　in　FGM　halfspaces.　The　penny-shaped　and　elliptical　cracks　are　horizontally　placed　on　the　interface　between　the　FGM　layer　and　homogeneous　halfspace　and　are　subjected　to　uniform　compressive　stresses　on　crack　surfaces.　The　stress　intensity　factors　are　provided　to　understand　the　fracture　behaviors　of　transversely　isotropic　FGMs.　An　influential　factor　is　defined　to　describe　the　influence　of　the　anisotropy　of　the　FGMs　on　stress　intensity　factors.　Results　show　that　the　anisotropy　and　heterogeneity　of　materials　exert　an　obvious　influence　on　the　fracture　properties　of　crack　problems.