In　this　paper,　a　new　and　efficient　Dual　Boundary　Element　Method　(DBEM)　named　Dual　Boundary-Interface　Integral　Equation　Method　(DBIIEM)　is　presented　to　solve　crack　problems　in　objects　composed　of　arbitrary　number　of　different　materials.　The　conventional　DBEM　has　been　widely　used　in　crack　analysis　and　proved　to　be　one　of　the　most　effective　BEM　for　solving　crack　problems,　however　it　cannot　be　directly　employed　to　solve　more　complicated　multi-medium　crack　problems.　The　presented　DBIIEM　can　remedy　this　deficiency　by　dually　collocating　the　displacement　boundary-interface　integral　equation　on　one　of　the　multi-medium　crack　surface　and　traction　boundary-interface　integral　equation　on　the　other.　The　newly　derived　displacement　and　traction　boundary-interface　integral　equations　are　naturally　fit　for　solving　multi-medium　elasticity　problems,　and　independent　each　other,　therefore　they　can　be　employed　together　in　multi-medium　crack　analysis.　The　established　DBIIEM　inherits　the　advantage　of　single　-region　formulation　of　DBEM　for　solving　more　complicated　crack　problems.　Complex　stress　intensity　factors　which　characterize　the　oscillatory　singularity　of　crack　tips　located　at　the　interface　crack　are　evaluated.　Several　numerical　examples　are　given　to　verify　correctness　of　the　presented　method.　©　2020