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A spatial images technique is used to efficiently calculate the mixed potential Green's functions associated to magnetic sources when they are placed inside a circular cylindrical cavity. The technique places magnetic dipole images and charges outside the cylindrical region. Their strength and orientation are then calculated by imposing the appropriate boundary conditions for the fields at discrete points of the metallic wall. In this paper, the basic technique is combined with spatial domain multilayered Green's functions formulated with Sommerfeld integrals. This allows the analysis of practical multilayered circuits shielded in circular cavities. Convergence results are shown to demonstrate the usefulness of the technique. Two practical microwave circuits are also analyzed to show the validity of the formulation.