A new technique of implementing dual-bandpass filters built on rectangular dielectric resonators has been proposed. The possibility of simultaneous tuning of two passbands on one structure of coupled dielectric resonators using their intrinsic high-mode oscillations was investigated for the sake of reducing the size of design. The proposed analytical solution was compared with the results of simulation by the finite element method. Coupling coefficients of rectangular resonators were calculated and investigated by a numeric technique for the low dipole TE 01δ and high quadruple TE 02δ magnetic modes depending on the parameters of filter design. The proposed dual-bandpass filter built on dielectric resonators can be used in base stations and wireless access points of communication networks.