In　this　paper,　an　improvement　is　made　to　an　efficient　direct　method　for　numerical　evaluation　of　high　order　singular　curved　boundary　integrals.　Then　this　improved　singular　integral　evaluation　method　is　employed　to　solve　the　strongly　and　hypersingular　integrals　involved　in　the　dual　boundary　element　method　(Dual　BEM),　which　combine　the　use　of　displacement　and　traction　boundary　integral　equations　to　solve　crack　problems　in　a　single　domain　formulation.　The　singular　integral　evaluation　method　is　carried　out　based　on　a　parameter　plane　expansion　and　radial　integral　approach,　this　paper　proposed　a　new　strategy　for　treating　the　singular　radial　integral,　which　plays　a　vital　role　in　this　method.　In　isoparametric　coordinate　system,　the　singular　curved　boundary　integral　is　mapped　into　a　singular　square　plane　integral　in　intrinsic　coordinates,　then　the　radial　integration　method　(RIM)　is　employed　to　transform　the　singular　square　plane　integral　into　a　regular　line　integral　over　the　contour　of　intrinsic　square　plane　and　a　singular　radial　integral　over　the　path　from　source　point　to　the　contour　of　intrinsic　square　plane.　A　singularity　isolation　technique　is　utilized　to　divide　the　singular　radial　integral　into　two　parts,　the　regular　radial　integral　can　be　evaluated　normally　using　Gauss　quadrature　and　the　singular　radial　that　can　be　evaluated　analytically　by　expanding　the　non-singular　part　of　the　integrand　function　into　a　power　series.　Compared　with　conventional　local　interpolation　approach　to　deal　with　the　singular　radial　integral,　the　newly　proposed　method　has　a　more　rigorous　mathematical　derivation,　and　can　achieve　more　stable　and　precise　results.　Based　on　the　successful　implementation　of　direct　evaluation　of　singular　boundary　integrals,　Dual　BEM　is　successfully　applied　to　solve　twoand　three-dimensional　elastic　crack　problems　including　straight　and　curved　crack　paths　with　continuous　or　discontinuous　elements.　Two　different　approaches,　geometrical　extrapolation　method　and　J-integral　method　are　used　in　the　evaluation　of　stress　intensity　factors.　Several　numerical　examples　are　given　to　validate　effectiveness　of　the　presented　method.