The weakly singular integral equation used to solve the problem of the curved crack crossing the boundary of the antiplane circular inclusion is presented. Using the principal part analysis method of the Cauchy type integral equation, the singular stress index at the intersection and the singular stress of angular regions near the intersection are obtained. By using the singular stress obtained, the stress intensity factor at the intersection is defined. After the numerical solution of the integral equation, the stress intensity factors at the end points of the crack and intersection are obtainable.