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A semi-analytical approach for analyzing two-dimensional electromagnetic scattering by layered cylindrical arrays of circular rods periodically distributed along concentrically layered circular rings is presented. The method uses the T-matrix of a circular rod in isolation, the reflection and transmission matrices of a cylindrical array expressed in terms of the cylindrical harmonic waves as the basis and the generalized reflection and transmission matrices for a layered cylindrical structure. Using the method, the scattering of plane waves impinging on the cylindrical arrays from the exterior region and the radiation from a line source located inside the cylindrical arrays are numerically investigated. Numerical examples demonstrate that the layered cylindrical arrays are effective for forming a directed beam in the scattered and radiated fields.