In this paper, a new efficient Dual Boundary Element Method (Dual BEM) named Dual Boundary-Interface Integral Equation Method (DBIIEM) is proposed to solve crack problems in objects composed of arbitrary number of multiple media. The presented DBIIEM retains the advantage of the widely used Dual BEM for solving crack problems in a form of single region formulation, but makes up for the lack of Dual BEM in solving crack problems in arbitrary dissimilar materials.