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The interaction between an elastic rectangular inclusion and a kinked crack in an infinite elastic body was considered by using boundary element method. The new complex boundary integral equations were derived. By introducing a complex unknown function H(t) related to the interface displacement density and traction and applying integration by parts, the traction continuous condition was satisfied automatically. Only one complex boundary integral equation was obtained on interface and involves only singularity of order 1/r. To verify the validity and effectiveness of the present boundary element method, some typical examples were calculated. The obtained results show that the crack stress intensity factorsdecrease as the shear modulus of inclusion increases. Thus, the crack propagation is easier near a softer inclusion and the harder inclusion is helpful for crack arrest.