By using of complex variable function and integral equation method, the interaction between antiplane circular inclusion and multiple holes and multiple cracks is considered in this paper. In order to solve the proposed problem, two kinds of elementary solution are presented. Utilizing the proposed elementary solutions and taking density functions of elementary solutions along holes' and cracks' surface as undetermined functions, a group of Fredholm integral equations can be established. After the numerical solution of the integral equations, the SIF values at the cracks' tips can be calculated.