We demonstrate that a circular dielectric cylinder can be nearly invisible at multiple frequencies when being coated with a ring shell, which is made of an isotropic material simultaneously showing large positive or large negative values of permittivity and permeability. The suggested cloaking mechanism is based on the use of radial resonances, which are similar to those in conventional Fabry-Perot resonators. It can be used for cylindrical objects for a wide range of variation of the diameter-to-wavelength ratio, which includes the values corresponding to subwavelength to resonant-sized objects. The presence of frequency dispersion of the shell material positively affects the possibility of multifrequency operation.