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Closed-form Green's functions for cylindrically stratified media are derived in terms of spherical waves and surface-wave contributions. The methodology is based on a two-level approximation of the spectral-domain Green's functions. In the first step, the large argument behavior of the zeroth-order Hankel functions is used for the extraction of the quasistatic images from the spectral-domain Green's functions with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated in terms of pole-residue expressions via the rational function fitting method. This robust, efficient, and fully numerical approach does not call for an analytical cumbersome extraction of the surface wave poles, prior to the spectrum fitting. Moreover, it can be applied in both the near- and far-field. Numerical results for the Green's functions of one-layer and two-layer structures are presented to verify the accuracy and efficiency of this approach.