In this paper, the torsion problem of a composite cylinder with cracks and inclusions is investigated. Firstly, a linear inclusion model is proposed and the fundamental solution of this model is obtained. With the help of this solution together with Muskhelishvili's single-layer potential function and the fundamental solution of a single crack, the torsion problem can be reduced to solving a set of mixed-type integral equations, then the numerical method of these equations is proposed. At the end, several numerical examples are calculated and the results are satisfactory.