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A method of fast computation of the mixed potential Green's functions (MPGFs) in spatial domain for cylindrically stratified media has been developed. Based on the convergence behavior of the MPGFs in spectral domain, the discrete complex image method (DCIM) and the extrapolation technique are employed to perform the inverse Fourier transform, which is different from that of planarly stratified media. In order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity, the Green's functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process. For the integral along the deformed Sommerfeld integral path with respect to kz, DCIM is used to speed up the computation. After the quasistatic components are completely subtracted from the spectral domain Green's functions, the inverse transform of the remaining parts has an approximated analytical form. The proposed method can be used to accurately and efficiently calculate the spatial domain MPGFs, which are useful for characterizing conformal patch structures mounted on cylindrically stratified media.