The axially symmetric problem of an infinite elastic fiber embedded into an infinite matrix of different thermomechanical properties is considered. It is assumed that the composite contains imperfections in the form of interface cracks or a broken fiber. The integral equations for the singular part of the problem are obtained by considering concentrated dislocations on the fiber-matrix interface and using the results as Green’s functions. The resulting system of singular integral equations is solved, the expressions for stress intensity factors at the points of singularity and the strain-energy release rate are obtained, and a numerical example is given.