A microcrack can be initiated by coalescing dislocations piled up near an inhomogeneity. This mechanism was firstly proposed by Zener and later analyzed by Stroh. The microcrack thus is called a Zener-Stroh crack, a counterpart of the well-known Griffith crack in linear elastic fracture mechanics. In the current study we consider a Zener-Stroh crack initiated near a coated circular fiber in a solid material. The interaction between the crack and the coated inclusion (fiber) for both Mode I and II displacement loading is investigated using the solution of an edge dislocation interacting with a coated fiber derived by Xiao and Chen [International Journal of Solids and Structure, in press] as the Green's function. The problem is formulated as a set of singular integral equations and is solved numerically by Erdogan-Gupta method. The influence of several parameters, such as the distance between the crack and the inclusion, the material constants combination of the fiber, the coating layer and the matrix, on the stress intensity factors of the crack is analyzed. Several numerical examples are given and the results obtained are discussed in detail.