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An algorithm using 2 x 2 matrices to compute the response of an arbitrary point source in the vicinity of a multicylindrically ally layered medium is presented. The algorithm is physical and efficient and can be implemented easily for any number of layers, and with the source location in any of the layers. The formalism can be easily extended to related structures and the algorithm has potential applications in the areas of optics, defense, and geophysical exploration. It also corresponds to finding the Green's function to the multicylindrically layered geometry. Reflection and transmission coefficients are defined such that a simple recursive algorithm can be given to determine the fields in all the layers.