Abstract: According to the theory of Saint-Venant's torsion, a fundamental solutionof a linear inclusion model proposed in this paper is obtained, which will be useful to the torsion problem. Using the obtained solution together with the Muskhelishvili's potential solution of single layer and the fundamental solution of a single crack, the torsion problem of a composite-cylinder with crack and inclusion is studied. Finally, the problem is reduced to solving a set of mixed-type integral equations and at the same time ...