A numerical method based on the coupling of the finite difference method in the time domain with the discrete Fourier transform, is presented and is applicable to axially symmetrical resonant systems. An appropriate treatment of the resultant Fourier coefficients provides the frequency spectrum and the spatial distribution of the modes defined in the structure. The validity of the method has been shown by applying it to systems of a known analytical solution: a homogeneous cavity and a cavity dielectrically loaded at its base.