The Green's functions of grounded magnetodielectric slabs with LE, LM waves' expansion and layered circular cylinder with E, H waves' expansion are used for surface and space waves analysis. Traditional magnetodielectrics and double negative materials are under consideration. Radiation patterns of surface waves excited by a slot covered with double-positive and double-negative permittivity and permeability media are obtained. A scattering from covered cylinder are considered. Angularities of back scattering coefficient are connected with azimuth electrical current resonances.