To　evaluate　the　crack-tip　field　intensity　factors　of　a　piezoelectric　crack　with,　any　inclined　angle,　the　current　widely-used　interaction　integral　method　(I-integral)　is　here　extended　to　the　boundary　element　applications　under　some　coordinate　transformations.　As　well,　a　new　modified　crack　closure　integral　method　(MCCI)　is　proposed　by　considering　the　discontinuous　quarter-point　singular　elements　for　the　crack-face　discretization　arising　from　the　dual　boundary　element　method　(BEM).　This　dual　BEM　involves　the　strongly　singular　displacement　boundary　integral　equations　(BIEs)　for　the　external　boundary　and　the　hypersingular　traction　BIEs　for　the　crack　faces.　The　crack-tip　fracture　parameters　evaluated　by　the　I-integral　and　MCCI　are　verified　by　the　existing　analytical　solutions　and　meanwhile,　compared　with　those　results　achieved　by　the　classical　displacement　extrapolation　method　and　the　J-integral.　Three　examples　are　presented　to　show　the　high　accuracy　of　the　interaction　integral　method　and　the　improvement　of　MCCI　for　the　piezoelectric　crack　problems.