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The electromagnetic scattering from a conducting object coated with metamaterials, which have both negative permittivity and permeability is derived rigorously by using finite difference frequency domain (FDFD). A formulation for the FDFD method is presented. The scattering from circular and multilayers elliptic cylinder coated by metamaterial are investigated. Also, the scattering from dielectric and metamaterial sphere is depicted. Numerical results are compared with the available data in the literature.