In this study, the diffraction of a plane wave by an infinitely long strip, having the same impedance on both faces with a width of 2a is investigated. The diffracted field is expressed by an integral in terms of the induced electric and magnetic current densities. Applying the boundary condition to the integral representation of the scattered field, the problem is formulated as simultaneous integral equations satisfied by the electric and magnetic current density functions. By obtaining the Fourier transform of the integral equations the unknown current density functions can be expanded into the infinite series containing the Chebyshev polynomials. This leads to two infinite systems of linear algebraic equations satisfied by the expansion coefficients. These coefficients are determined numerically with high accuracy via appropriate truncation of the systems of linear algebraic equations. Evaluating the scattered field asymptotically, a far field expression is derived. Some illustrative numerical examples on the monostatic and bistatic radar cross section (RCS) are presented and the far field scattering characteristics are discussed.